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Optimization and nonsmooth analysis
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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
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Journal ArticleDOI
Uniform exponential convergence of sample average random functions under general sampling with applications in stochastic programming
TL;DR: This paper derives the uniform exponential convergence of the sample average of a class of lower semicontinuous random functions and applies it to a nonsmooth stochastic minimization problem and uses the unform convergence result to establish the exponential rate of convergence of statistical estimators of a stochastics Nash equilibrium problem and estimator of the solutions to a Stochastic generalized equation problem.
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Hunting for a Smaller Convex Subdifferential
TL;DR: It is shown that there existsubdifferentials which may be smaller than the Michel–Penot subdifferential and which have certain useful calculus which hold for the Clarke sub differential only in the regular case.
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Nonsmooth multiobjective programming
TL;DR: In this article, necessary Lagrangian conditions are obtained for a weak minimum of a nonsmooth constrained multiobjective programming problem, assuming Lipschitz functions and general cone constraints.
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Constrained Quaternion-Variable Convex Optimization: A Quaternion-Valued Recurrent Neural Network Approach
TL;DR: The rigorous analysis shows that the deliberately designed quaternion-valued one-layer recurrent neural network stabilizes the system dynamics while the states reach the feasible region in finite time and converges to the optimal solution of the considered constrained convex optimization problems finally.
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Mixed Variable Optimization of the Number and Composition of Heat Intercepts in a Thermal Insulation System
TL;DR: In this paper, thermal insulation systems with a fixed number of heat intercepts have been optimized with respect to intercept locations and temperatures, and the number of intercepts and the types of insulators that surround them were chosen by parametric studies.