Open AccessBook
Optimization and nonsmooth analysis
TLDR
The Calculus of Variations as discussed by the authors is a generalization of the calculus of variations, which is used in many aspects of analysis, such as generalized gradient descent and optimal control.Abstract:
1. Introduction and Preview 2. Generalized Gradients 3. Differential Inclusions 4. The Calculus of Variations 5. Optimal Control 6. Mathematical Programming 7. Topics in Analysis.read more
Citations
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Algorithms for complementarity problems and generalized equations
TL;DR: In this article, a proximal perturbation strategy is proposed to improve the robustness of Newton-based complementarity solvers, which enables algorithms to reliably find solutions even for problems whose natural merit functions have strict local minima.
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Proximally Guided Stochastic Subgradient Method for Nonsmooth, Nonconvex Problems
Damek Davis,Benjamin Grimmer +1 more
TL;DR: A simple proof that the proposed algorithm converges at the same rate as the stochastic gradient method for smooth nonconvex problems is presented, which appears to be the first convergence rate analysis of a Stochastic subgradient method for the class of weakly convex functions.
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Parallel Space Decomposition of the Mesh Adaptive Direct Search Algorithm
TL;DR: A parallel space decomposition PSD technique for the mesh adaptive direct search MADS algorithm and some numerical results on problems with up to 500 variables illustrate the advantages and limitations of PSD-MADS.
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On the Coderivative of the Projection Operator onto the Second-order Cone
Jiří V. Outrata,Defeng Sun +1 more
TL;DR: In this article, a sufficient condition for the Aubin property of the solution map of a parameterized second-order cone complementarity problem was derived for a mathematical program with a secondorder cone complearity problem among the constraints.
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Regularized Equilibrium Problems with Application to Noncoercive Hemivariational Inequalities
TL;DR: In this article, a regularization procedure for non-coercive equilibrium problems with a bifunction which does not satisfy necessarily an algebraic monotonicity assumption is presented.