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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 Numerical Approach to Optimal Coherent Quantum LQG Controller Design Using Gradient DescentSep 24 2016This paper is concerned with coherent quantum linear quadratic Gaussian (CQLQG) control. The problem is to find a stabilizing measurement-free quantum controller for a quantum plant so as to minimize a mean square cost for the fully quantum closed-loop ... More

Energy-conserving time-discretisation of abstract dynamic problems with applications in continuum mechanics of solidsMay 31 2016An abstract 2nd-order evolution equation or inclusion is discretised in time in such a way that the energy is conserved at least in qualified cases, typically in the cases when the governing energy is component-wise quadratic or "slightly-perturbed" quadratic. ... More

Stress-driven solution to rate-independent elasto-plasticity with damage at small strains and its computer implementationJun 03 2015The quasistatic rate-independent damage combined with linearized plasticity with hardening at small strains is investigated. The fractional-step time discretisation is devised with the purpose to obtain a numerically efficient scheme converging possibly ... More

Perfect plasticity with damage and healing at small strains, its modelling, analysis, and computer implementationMay 05 2015The quasistatic, Prandtl-Reuss perfect plasticity at small strains is combined with a gradient, reversible (i.e. admitting healing) damage which influences both the elastic moduli and the yield stress. Existence of weak solutions of the resulted system ... More

A Gradient Descent Approach to Optimal Coherent Quantum LQG Controller DesignFeb 01 2015This paper is concerned with the Coherent Quantum Linear Quadratic Gaussian (CQLQG) control problem of finding a stabilizing measurement-free quantum controller for a quantum plant so as to minimize an infinite-horizon mean square performance index for ... More

Adaptive Augmented Lagrangian Methods: Algorithms and Practical Numerical ExperienceAug 20 2014In this paper, we consider augmented Lagrangian (AL) algorithms for solving large-scale nonlinear optimization problems that execute adaptive strategies for updating the penalty parameter. Our work is motivated by the recently proposed adaptive AL trust ... More

Alternating Projections and Douglas-Rachford for Sparse Affine FeasibilityJul 08 2013Mar 14 2014The problem of finding a vector with the fewest nonzero elements that satisfies an underdetermined system of linear equations is an NP-complete problem that is typically solved numerically via convex heuristics or nicely-behaved nonconvex relaxations. ... More