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Stochastic subgradient method converges at the rate $O(k^{-1/4})$ on weakly convex functionsFeb 08 2018We prove that the projected stochastic subgradient method, applied to a weakly convex problem, drives the gradient of the Moreau envelope to zero at the rate $O(k^{-1/4})$.
A New Kalman Filter Model for Nonlinear Systems Based on Ellipsoidal BoundingFeb 08 2018In this paper, a new filter model called set-membership Kalman filter for nonlinear state estimation problems was designed, where both random and unknown but bounded uncertainties were considered simultaneously in the discrete-time system. The main loop ... More
Solving Linear Programs with Complementarity Constraints using Branch-and-CutFeb 08 2018A linear program with linear complementarity constraints (LPCC) requires the minimization of a linear objective over a set of linear constraints together with additional linear complementarity constraints. This class has emerged as a modeling paradigm ... More
Lower Bounds for the Fair Resource Allocation ProblemFeb 08 2018The $\alpha$-fair resource allocation problem has received remarkable attention and has been studied in numerous application fields. Several algorithms have been proposed in the context of $\alpha$-fair resource sharing to distributively compute its value. ... More
Primal-dual stochastic gradient method for convex programs with many functional constraintsFeb 08 2018Stochastic gradient (SG) method has been popularly applied to solve optimization problems with objective that is stochastic or an average of many functions. Most existing works on SG assume that the underlying problem is unconstrained or has an easy-to-project ... More
Exact Semidefinite Formulations for a Class of (Random and Non-Random) Nonconvex Quadratic ProgramsFeb 08 2018We study a class of quadratically constrained quadratic programs (QCQPs), called {\em diagonal QCQPs\/}, which contain no off-diagonal terms $x_j x_k$ for $j \ne k$, and we provide a sufficient condition on the problem data guaranteeing that the basic ... More
A diffusion generated method for computing Dirichlet partitionsFeb 08 2018A Dirichlet $k$-partition of a closed $d$-dimensional surface is a collection of $k$ pairwise disjoint open subsets such that the sum of their first Laplace-Beltrami-Dirichlet eigenvalues is minimal. In this paper, we develop a simple and efficient diffusion ... More
Fast methods for nonsmooth nonconvex minimizationFeb 07 2018We propose a new class of algorithms for nonsmooth, nonconvex problems that are expressible as compositions of nonsmooth nonconvex functions with smooth maps. In many cases, these algorithms require only (1) least squares solvers and (2) proximal operators ... More
Manifold Optimization Over the Set of Doubly Stochastic Matrices: A Second-Order GeometryFeb 07 2018Convex optimization is a well-established research area with applications in almost all fields. Over the decades, multiple approaches have been proposed to solve convex programs. The development of interior-point methods allowed solving a more general ... More
An improved multi-parametric programming algorithm for flux balance analysis of metabolic networksFeb 07 2018Flux balance analysis (FBA) has proven an effective tool for analyzing metabolic networks. In FBA, reaction rates and optimal pathways are ascertained by solving a linear program, in which the growth rate is maximized subject to mass-balance constraints. ... More
A global linear and local superlinear/quadratic inexact non-interior continuation method for variational inequalitiesFeb 07 2018We use the concept of barrier-based smoothing approximations introduced by Chua and Li \cite{Chua_Li} to extend the non-interior continuation method proposed by Chen and Xiu \cite{Bintong} to an inexact non-interior continuation method for variational ... More
Local Convergence Properties of SAGA/Prox-SVRG and AccelerationFeb 07 2018Over the past ten years, driven by large scale optimisation problems arising from machine learning, the development of stochastic optimisation methods have witnessed a tremendous growth. However, despite their popularity, the theoretical understandings ... More
A Dynamic Programming Approach to Evaluating Multivariate Gaussian ProbabilitiesFeb 07 2018We propose a method of approximating multivariate Gaussian probabilities using dynamic programming. We show that solving the optimization problem associated with a class of discrete-time finite horizon Markov decision processes with non-Lipschitz cost ... More
BROJA-2PID: A robust estimator for bivariate partial information decompositionFeb 07 2018Makkeh, Theis, and Vicente found in [8] that Cone Programming model is the most robust to compute the Bertschinger et al. partial information decompostion (BROJA PID) measure [1]. We developed a production-quality robust software that computes the BROJA ... More
A polynomial time algorithm for the linearization problem of the QSPP and its applicationsFeb 07 2018Given an instance of the quadratic shortest path problem (QSPP) on a digraph $G$, the linearization problem for the QSPP asks whether there exists an instance of the linear shortest path problem on $G$ such that the associated costs for both problems ... More
Definable Ellipsoid Method, Sums-of-Squares Proofs, and the Isomorphism ProblemFeb 07 2018The ellipsoid method is an algorithm that solves the (weak) feasibility and linear optimization problems for convex sets by making oracle calls to their (weak) separation problem. We observe that the previously known method for showing that this reduction ... More
Improved Oracle Complexity of Variance Reduced Methods for Nonsmooth Convex Stochastic Composition OptimizationFeb 07 2018Feb 08 2018We consider the nonsmooth convex composition optimization problem where the objective is a composition of two finite-sum functions and analyze stochastic compositional variance reduced gradient (\textsf{SCVRG}) methods for them. \textsf{SCVRG} and its ... More
Reduced basis approximation and a~posteriori error bounds for 4D-Var data assimilationFeb 07 2018We propose a certified reduced basis approach for the strong- and weak-constraint four-dimensional variational (4D-Var) data assimilation problem for a parametrized PDE model. While the standard strong-constraint 4D-Var approach uses the given observational ... More
An example showing that A-lower semi-continuity is essential for minimax continuity theoremsFeb 07 2018Recently Feinberg et al. [arXiv:1609.03990] established results on continuity properties of minimax values and solution sets for a function of two variables depending on a parameter. Such minimax problems appear in games with perfect information, when ... More
On the sum of projectors onto convex setsFeb 07 2018The projector onto the Minkowski sum of closed convex sets is generally not equal to the sum of individual projectors. In this work, we provide a complete answer to the question of characterizing the instances where such an equality holds. Our results ... More
Second order backward SDE with random terminal timeFeb 06 2018Backward stochastic differential equations extend the martingale representation theorem to the nonlinear setting. This can be seen as path-dependent counterpart of the extension from the heat equation to fully nonlinear parabolic equations in the Markov ... More
Approximation Methods for Bilevel ProgrammingFeb 06 2018In this paper, we study a class of bilevel programming problem where the inner objective function is strongly convex. More specifically, under some mile assumptions on the partial derivatives of both inner and outer objective functions, we present an ... More
Polynomial algorithm for k-partition minimization of submodular system with strong symmetryFeb 06 2018For a fixed $k$, this study considers $k$-partition minimization of submodular system $(V, f)$ with a finite set $V$ and symmetric submodular function $f: 2^{V} \mapsto \mathbb{R}$ with {\it strong symmetry}, which holds $f(U_{0}) = f( U_{1} \setminus ... More
Integrated design optimization of structural bending filter and gain schedules for rocket attitude control systemFeb 06 2018This paper proposes an integrated design optimization framework for the gain schedules and bending filter for the longitudinal control of a rocket during its ascent flight. Dynamic models representing the pitch/yaw motion of a rocket considering the elements ... More
About the Noether's theorem for fractional Lagrangian systems and a generalization of the classical Jost method of proofFeb 05 2018Recently, the fractional Noether's theorem derived by G. Frederico and D.F.M. Torres in Appl. Math. Comp. 217,3,2010 was proved to be wrong by R.A.C. Ferreira and A.B. Malinowska in JMAA 429, 2, 2015 using a counterexample and doubts are stated about ... More
Optimal consensus control of the Cucker-Smale modelFeb 05 2018We study the numerical realisation of optimal consensus control laws for agent-based models. For a nonlinear multi-agent system of Cucker-Smale type, consensus control is cast as a dynamic optimisation problem for which we derive first-order necessary ... More
Linear Convergence of the Primal-Dual Gradient Method for Convex-Concave Saddle Point Problems without Strong ConvexityFeb 05 2018We consider the convex-concave saddle point problem $\min_{x}\max_{y} f(x)+y^\top A x-g(y)$ where $f$ is smooth and convex and $g$ is smooth and strongly convex. We prove that if the coupling matrix $A$ has full column rank, the vanilla primal-dual gradient ... More
How to Characterize the Worst-Case Performance of Algorithms for Nonconvex OptimizationFeb 04 2018A proposal is presented for how to characterize the worst-case performance of algorithms for solving smooth nonconvex optimization problems. Contemporary analyses characterize worst-case performance by providing, under certain broad assumptions on the ... More
Lyapunov Design for Event-Triggered Exponential StabilizationFeb 03 2018Control Lyapunov Functions (CLF) method gives a constructive tool for stabilization of nonlinear systems. To find a CLF, many methods have been proposed in the literature, e.g. backstepping for cascaded systems and sum of squares (SOS) programming for ... More
Representations of quadratic combinatorial optimization problems: A case study using the quadratic set covering problemFeb 03 2018The objective function of a quadratic combinatorial optimization problem (QCOP) can be represented by two data points, a quadratic cost matrix Q and a linear cost vector c. Different, but equivalent, representations of the pair (Q, c) for the same QCOP ... More
On computational issues for stability analysis of LPV systems using parameter dependent Lyapunov functions and LMIsFeb 02 2018This paper deals with the robust stability analysis of linear systems, subject to time-varying parameters. The Parameter Dependent Lyapunov Function are considered, assuming that the temporal derivative of the parameters are bounded. Some computational ... More
Privacy of Information Sharing Schemes in a Cloud-based Multi-sensor Estimation ProblemFeb 02 2018In this paper, we consider a multi-sensor estimation problem wherein each sensor collects noisy information about its local process, which is only observed by that sensor, and a common process, which is simultaneously observed by all sensors. The objective ... More
A Unifying Theory of Exactness of Linear Penalty FunctionsFeb 01 2018In this article we develop a theory of exact linear penalty functions that generalizes and unifies most of the results on exact penalization existing in the literature. We discuss several approaches to the study of both locally and globally exact linear ... More
The Barycenter Method for Direct OptimizationJan 31 2018A randomized version of the recently developed barycenter method for derivative-free optimization has desirable properties of a gradient search. We develop a complex version to avoid evaluations at high-gradient points. The method, applicable to non-smooth ... More
A Simple Adaptive Step-size Choice for Iterative Optimization MethodsJan 31 2018We suggest a simple adaptive step-size procedure for a general class of iterative optimization methods, which does not require any line-search, and prove convergence of a general method under mild assumptions. This procedure maintains the basic convergence ... More
Optimal Configurations in Coverage Control with Polynomial CostsJan 31 2018We revisit the static coverage control problem for placement of vehicles with simple motion on the real line, under the assumption that the cost is a polynomial function of the locations of the vehicles. The main contribution of this paper is to demonstrate ... More
Compressed Anomaly Detection with Multiple Mixed ObservationsJan 31 2018We consider a collection of independent random variables that are identically distributed, except for a small subset which follows a different, anomalous distribution. We study the problem of detecting which random variables in the collection are governed ... More
Analysis and optimal control of an intracellular delayed HIV model with CTL immune responseJan 30 2018A delayed model describing the dynamics of HIV (Human Immunodeficiency Virus) with CTL (Cytotoxic T Lymphocytes) immune response is investigated. The model includes four nonlinear differential equations describing the evolution of uninfected, infected, ... More
Parameter Estimation, Sensitivity Analysis and Optimal Control of a Periodic Epidemic Model with Application to HRSV in FloridaJan 29 2018A state wide Human Respiratory Syncytial Virus (HRSV) surveillance system was implemented in Florida in 1999 to support clinical decision-making for prophylaxis of premature infants. The research presented in this paper addresses the problem of fitting ... More
Using deep Q-learning to understand the tax evasion behavior of risk-averse firmsJan 29 2018Designing tax policies that are effective in curbing tax evasion and maximize state revenues requires a rigorous understanding of taxpayer behavior. This work explores the problem of determining the strategy a self-interested, risk-averse tax entity is ... More
Modified lp-norm regularization minimization for sparse signal recoveryJan 28 2018In numerous substitution models for the $\l_{0}$-norm minimization problem $(P_{0})$, the $\l_{p}$-norm minimization $(P_{p})$ with $0<p<1$ have been considered as the most natural choice. However, the non-convex optimization problem $(P_{p})$ are much ... More
A Redesigned Benders Decomposition Approach for Large-Scale In-Transit Freight Consolidation OperationsJan 26 2018The growth in online shopping and third party logistics has caused a revival of interest in finding optimal solutions to the large scale in-transit freight consolidation problem. Given the shipment date, size, origin, destination, and due dates of multiple ... More
Event-triggered stabilization of disturbed linear systems over digital channelsJan 26 2018We present an event-triggered control strategy for stabilizing a scalar, continuous-time, time-invariant, linear system over a digital communication channel having bounded delay, and in the presence of bounded system disturbance. We propose an encoding-decoding ... More
Improved Finite Blocklength Converses for Slepian-Wolf Coding via Linear ProgrammingJan 26 2018A new finite blocklength converse for the Slepian- Wolf coding problem is presented which significantly improves on the best known converse for this problem, due to Miyake and Kanaya [2]. To obtain this converse, an extension of the linear programming ... More
FLORIS and CLORIS: Hybrid Source and Network Localization Based on Ranges and VideoJan 24 2018We propose hybrid methods for localization in wireless sensor networks fusing noisy range measurements with angular information (extracted from video). Compared with conventional methods that rely on a single sensed variable, this may pave the way for ... More
Statistical Learning For DC Optimal Power FlowJan 23 2018The optimal power flow problem plays an important role in the market clearing and operation of electric power systems. However, with increasing uncertainty from renewable energy operation, the optimal operating point of the system changes more significantly ... More
Smooth exact penalty functions II: a reduction to standard exact penalty functionsJan 23 2018Jan 29 2018A new class of smooth exact penalty functions was recently introduced by Huyer and Neumaier. In this paper, we prove that the new smooth penalty function for a constrained optimization problem is exact if and only if the standard nonsmooth penalty function ... More
A convergence analysis of the method of codifferential descentJan 23 2018This paper is devoted to a detailed convergence analysis of the method of codifferential descent (MCD) developed by professor V.F. Demyanov for solving a large class of nonsmooth nonconvex optimization problems. We propose a generalization of the MCD ... More
A Proximal Approach for a Class of Matrix Optimization ProblemsJan 23 2018In recent years, there has been a growing interest in mathematical models leading to the minimization, in a symmetric matrix space, of a Bregman divergence coupled with a regularization term. We address problems of this type within a general framework ... More
Global Solution Strategies for the Network-Constrained Unit Commitment Problem with AC Transmission ConstraintsJan 22 2018We propose a novel global solution algorithm for the network-constrained unit commitment (NCUC) problem incorporating a nonlinear alternating current (AC) model of the transmission network, which is a mixed-integer quadratically constrained quadratic ... More
Global Deterministic Optimization with Artificial Neural Networks EmbeddedJan 22 2018Artificial neural networks (ANNs) are used in various applications for data-driven black-box modeling and subsequent optimization. Herein, we present an efficient method for deterministic global optimization of ANN embedded optimization problems. The ... More
Uniform asymptotic stability of a fractional tuberculosis modelJan 22 2018We propose a Caputo type fractional-order mathematical model for the transmission dynamics of tuberculosis (TB). Uniform asymptotic stability of the unique endemic equilibrium of the fractional-order TB model is proved, for any $\alpha \in (0, 1)$. Numerical ... More
The Optimal Majority Threshold as a Function of the Variation Coefficient of the EnvironmentJan 21 2018Within the model of social dynamics determined by collective decisions in a stochastic environment (ViSE model), we consider the case of a homogeneous society consisting of classically rational economic agents (or homines economici, or egoists). We present ... More
A Tractable Approach for designing Piecewise Affine Policies in Two-stage Adjustable Robust OptimizationJan 21 2018We consider the problem of designing piecewise affine policies for two-stage adjustable robust linear optimization problems under right-hand side uncertainty. It is well known that a piecewise affine policy is optimal although the number of pieces can ... More
At What Frequency Should the Kelly Bettor Bet?Jan 20 2018We study the problem of optimizing the betting frequency in a dynamic game setting using Kelly's celebrated expected logarithmic growth criterion as the performance metric. The game is defined by a sequence of bets with independent and identically distributed ... More
A Tutorial on Modeling and Analysis of Dynamic Social Networks. Part IIJan 20 2018Recent years have witnessed a significant trend towards filling the gap between Social Network Analysis (SNA) and control theory. This trend was enabled by the introduction of new mathematical models describing dynamics of social groups, the development ... More
Smooth Exact Penalty Functions: A General ApproachJan 19 2018Jan 29 2018In this article we present a new perspective on the smooth exact penalty function proposed by Huyer and Neumaier that is becoming more and more popular tool for solving constrained optimization problems. Our approach to Huyer and Neumaier's exact penalty ... More
On optimal control of free boundary problems of obstacle typeJan 19 2018A numerical study of an optimal control formulation for a shape optimization problem governed by an elliptic variational inequality is performed. The shape optimization problem is reformulated as a boundary control problem in a fixed domain. The discretized ... More
Simplified Versions of the Conditional Gradient MethodJan 16 2018We suggest simple modifications of the conditional gradient method for smooth optimization problems, which maintain the basic convergence properties, but reduce the implementation cost of each iteration essentially. Namely, we propose the step-size procedure ... More
Block-coordinate primal-dual method for the nonsmooth minimization over linear constraintsJan 15 2018We consider the problem of minimizing a convex, separable, nonsmooth function subject to linear constraints. The numerical method we propose is a block-coordinate extension of the Chambolle-Pock primal-dual algorithm. We prove convergence of the method ... More
On strong homogeneity of a class of global optimization algorithms working with infinite and infinitesimal scalesJan 13 2018The necessity to find the global optimum of multiextremal functions arises in many applied problems where finding local solutions is insufficient. One of the desirable properties of global optimization methods is \emph{strong homogeneity} meaning that ... More
Aperiodic Sampled-Data Control via Explicit Transmission Mapping: A Set Invariance ApproachJan 13 2018Jan 17 2018Event-triggered and self-triggered control have been proposed in recent years as promising control strategies to reduce communication resources in Networked Control Systems (NCSs). Based on the notion of set-invariance theory, this note presents new self-triggered ... More
On projective and affine equivalence of sub-Riemannian metricsJan 12 2018Consider a smooth manifold $M$ equipped with a bracket generating distribution $D$. Two sub-Riemannian metrics on $(M,D)$ are said to be projectively (resp. affinely) equivalent if they have the same geodesics up to reparameterization (resp. up to affine ... More
Determining Projection Constants of Univariate Polynomial SpacesJan 12 2018The long-standing problem of minimal projections is addressed from a computational point of view. Techniques to determine bounds on the projection constants of univariate polynomial spaces are presented. The upper bound, produced by a linear program, ... More
Improved asynchronous parallel optimization analysis for stochastic incremental methodsJan 11 2018Jan 12 2018As datasets continue to increase in size and multi-core computer architectures are developed, asynchronous parallel optimization algorithms become more and more essential to the field of Machine Learning. Unfortunately, conducting the theoretical analysis ... More
Stochastic global maximum principle for general mean-field forward backward control systems with jumpsJan 10 2018This paper focuses on investigating a stochastic global maximum principle with recursive utilities, where the controlled state process is derived by a general mean-field forward backward stochastic differential equation with jumps. The necessary condition ... More
Minimal convex majorants of functions and Demyanov--Rubinov super(sub)differentialsJan 04 2018The primary goal of the paper is to establish characteristic properties of (extended) real-valued functions defined on normed vector spaces that admit the representation as the lower envelope of their minimal (with respect to pointwise ordering) convex ... More
A discrete event traffic model explaining the traffic phases of the train dynamics in a metro line system with a junctionJan 03 2018Jan 08 2018This paper presents a mathematical model for the train dynamics in a mass-transit metro line system with one symmetrically operated junction. We distinguish three parts: a central part and two branches. The tracks are spatially discretized into segments ... More
Gradient-based Optimization for Regression in the Functional Tensor-Train FormatJan 03 2018Jan 11 2018We consider the task of low-multilinear-rank functional regression, i.e., learning a low-rank parametric representation of functions from scattered real-valued data. Our first contribution is the development and analysis of an efficient gradient computation ... More
Input to State Stability of Bipedal Walking Robots: Application to DURUSJan 02 2018Bipedal robots are a prime example of systems which exhibit highly nonlinear dynamics, underactuation, and undergo complex dissipative impacts. This paper discusses methods used to overcome a wide variety of uncertainties, with the end result being stable ... More
Rate of convergence in periodic homogenization of Hamilton-Jacobi equations: the convex settingJan 01 2018We study the rate of convergence of $u^\epsilon$, as $\epsilon \to 0+$, to $u$ in periodic homogenization of Hamilton-Jacobi equations. Here, $u^\epsilon$ and $u$ are viscosity solutions to the oscillatory Hamilton-Jacobi equation and its effective equation ... More
Backstepping Control of Coupled Linear Parabolic PIDEs with Spatially-Varying CoefficientsDec 22 2017This paper considers the backstepping design of state feedback controllers for coupled linear parabolic partial integro-differential equations (PIDEs) of Volterra-type with distinct diffusion coefficients, spatially-varying parameters and mixed boundary ... More
Gradient Descent Learns One-hidden-layer CNN: Don't be Afraid of Spurious Local MinimaDec 03 2017We consider the problem of learning a one-hidden-layer neural network with non-overlapping convolutional layer and ReLU activation function, i.e., $f(\mathbf{Z}; \mathbf{w}, \mathbf{a}) = \sum_j a_j\sigma(\mathbf{w}^\top\mathbf{Z}_j)$, in which both the ... More
Coupled regularization with multiple data discrepanciesNov 30 2017We consider a class of regularization methods for inverse problems where a coupled regularization is employed for the simultaneous reconstruction of data from multiple sources. Applications for such a setting can be found in multi-spectral or multi-modality ... More
Tighter Lifting-Free Convex Relaxations for Quadratic Matching ProblemsNov 29 2017In this work we study convex relaxations of quadratic optimisation problems over permutation matrices. While existing semidefinite programming approaches can achieve remarkably tight relaxations, they have the strong disadvantage that they lift the original ... More
Robust Decentralized Secondary Frequency Control in Power Systems: Merits and Trade-OffsNov 20 2017Frequency regulation in power systems is conventionally performed by broadcasting a centralized signal to local controllers. As a result of the energy transition, technological advances, and the scientific interest in distributed control and optimization ... More
A Lie bracket approximation approach to distributed optimization over directed graphsNov 15 2017We consider a group of computation units trying to cooperatively solve a distributed optimization problem with shared linear equality and inequality constraints. Assuming that the computation units are communicating over a network whose topology is described ... More
A Market Mechanism for Virtual InertiaNov 13 2017One of the recognized principal issues brought along by the steadfast migration towards power electronic interfaced energy sources is the loss of rotational inertia. In conventional power systems, the inertia of the synchronous machines plays a crucial ... More
Sample average approximation with heavier tails II: localization in stochastic convex optimization and persistence results for the LassoNov 13 2017We present exponential finite-sample nonasymptotic deviation inequalities for the SAA estimator's near-optimal solution set over the class of \emph{convex} stochastic optimization problems with heavy-tailed random H\"older continuous functions in the ... More
Multiphase mean curvature flows with high mobility contrasts: a phase-field approach, with applications to nanowiresNov 10 2017The structure of many multiphase systems is governed by an energy that penalizes the area of interfaces between phases weighted by surface tension coefficients. However, interface evolution laws depend also on interface mobility coefficients. Having in ... More
Stochastic Greedy Algorithms For Multiple Measurement VectorsNov 05 2017Sparse representation of a single measurement vector (SMV) has been explored in a variety of compressive sensing applications. Recently, SMV models have been extended to solve multiple measurement vectors (MMV) problems, where the underlying signal is ... More
Hierarchical and Distributed Monitoring of Voltage Stability in Distribution NetworksOct 29 2017We consider the problem of quantifying and assessing the steady-state voltage stability in radial distribution networks. Our approach to the voltage stability problem is based on a local, approximate, and yet highly accurate characterization of the determinant ... More
Curvature-aided Incremental Aggregated Gradient MethodOct 24 2017We propose a new algorithm for finite sum optimization which we call the curvature-aided incremental aggregated gradient (CIAG) method. Motivated by the problem of training a classifier for a d-dimensional problem, where the number of training data is ... More
Optimal Rates for Learning with Nyström Stochastic Gradient MethodsOct 21 2017In the setting of nonparametric regression, we propose and study a combination of stochastic gradient methods with Nystr\"om subsampling, allowing multiple passes over the data and mini-batches. Generalization error bounds for the studied algorithm are ... More
Shape optimisation with nearly conformal transformationsOct 17 2017Oct 19 2017In shape optimisation it is desirable to obtain deformations of a given mesh without negative impact on the mesh quality. We propose a new algorithm using least square formulations of the Cauchy-Riemann equations. Our method allows to deform meshes in ... More
Coupling Brain-Tumor Biophysical Models and Diffeomorphic Image RegistrationOct 16 2017We present the SIBIA (Scalable Integrated Biophysics-based Image Analysis) framework for joint image registration and biophysical inversion and we apply it to analyse MR images of glioblastomas (primary brain tumors). In particular, we consider the following ... More
Partially Asynchronous Distributed Unmixing of Hyperspectral ImagesOct 06 2017So far, the problem of unmixing large or multitemporal hyperspectral dataset has been specifically addressed in the remote sensing literature only by a few dedicated strategies. Among them, some attempts have been made within a distributed estimation ... More
Global phase and magnitude synchronization of coupled oscillators with application to the control of grid-forming power invertersOct 02 2017Oct 03 2017In this work, we explore a new approach to synchronization of coupled oscillators. In contrast to the celebrated Kuramoto model we do not work in polar coordinates and do not consider oscillations of fixed magnitude. We propose a synchronizing feedback ... More
A note on preconditioning weighted linear least squares, with consequences for weakly-constrained variational data assimilationSep 26 2017The effect of preconditioning linear weighted least-squares using an approximation of the model matrix is analyzed, showing the interplay of the eigenstructures of both the model and weighting matrices. A small example is given illustrating the resulting ... More
On the error of a priori sampling: zero forcing sets and propagation timeSep 25 2017Zero forcing is an iterative process on a graph used to bound the maximum nullity. The process begins with select vertices as colored, and the remaining vertices can become colored under a specific color change rule. The goal is to find a minimum set ... More
On the use of the saddle formulation in weakly-constrained 4D-VAR data assimilationSep 19 2017This paper discusses the practical use of the saddle variational formulation for the weakly-constrained 4D-VAR method in data assimilation. It is shown that the method, in its original form, may produce erratic results or diverge because of the inherent ... More
When is a Convolutional Filter Easy To Learn?Sep 18 2017We analyze the convergence of (stochastic) gradient descent algorithm for learning a convolutional filter with Rectified Linear Unit (ReLU) activation function. Our analysis does not rely on any specific form of the input distribution and our proofs only ... More
The shortest way to visit all metro lines in ParisSep 13 2017Sep 19 2017What if $\{$a tourist, a train addict, Dr. Sheldon Cooper, somebody who likes to waste time$\}$ wants to visit all metro lines or carriages in a given network in a minimum number of steps? We study this problem with an application to the Parisian metro ... More
MIP Formulations for the Steiner Forest ProblemSep 04 2017The Steiner Forest problem is among the fundamental network design problems. Finding tight linear programming bounds for the problem is the key for both fast Branch-and-Bound algorithms and good primal-dual approximations. On the theoretical side, the ... More
Online Convolutional Dictionary LearningAug 31 2017Convolutional sparse representations are a form of sparse representation with a structured, translation invariant dictionary. Most convolutional dictionary learning algorithms to date operate in batch mode, requiring simultaneous access to all training ... More
Model based learning for accelerated, limited-view 3D photoacoustic tomographyAug 31 2017Recent advances in deep learning for tomographic reconstructions have shown great potential to create accurate and high quality images with a considerable speed-up. In this work we present a deep neural network that is specifically designed to provide ... More
Total variation regularization of multi-material topology optimizationAug 21 2017Nov 17 2017This work is concerned with the determination of the diffusion coefficient from distributed data of the state. This problem is related to homogenization theory on the one hand and to regularization theory on the other hand. An approach is proposed which ... More
A note on surjectivity of piecewise affine mappingsJul 27 2017Jan 22 2018A standard theorem in nonsmooth analysis states that a piecewise affine function $F:\mathbb R^n\rightarrow\mathbb R^n$ is surjective if it is coherently oriented in that the linear parts of its selection functions all have the same nonzero determinant ... More
Robust Pricing and Hedging around the GlobeJul 26 2017We consider the martingale optimal transport duality for c\`adl\`ag processes with given initial and terminal laws. Strong duality and existence of dual optimizers (robust semi-static superhedging strategies) are proved for a class of payoffs that includes ... More
Computation of Optimal Transport on Discrete Metric Measure SpacesJul 21 2017In this paper we investigate the numerical approximation of an analogue of the Wasserstein distance for optimal transport on graphs that is defined via a discrete modification of the Benamou--Brenier formula. This approach involves the logarithmic mean ... More