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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
Weak sharp minima in mathematical programming
James V. Burke,Michael C. Ferris +1 more
TL;DR: Weak sharp minima were introduced in this article to characterize the existence of non-unique solution sets for linear and quadratic convex programming problems and for the linear complementarity problem.
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Prox-regular functions in variational analysis
R. A. Poliquin,R. T. Rockafellar +1 more
TL;DR: The class of prox-regular functions covers all lsc, proper, convex functions, lower-C2 functions and strongly amenable functions, hence a large core of functions of interest in variational analysis and optimization as mentioned in this paper.
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Representing preferences with a unique subjective state space
TL;DR: In this article, the authors extend Kreps' 1979 analysis of preference for flexibility, reinterpreted by Kreps Ž.1992 as a model of unforeseen contingencies, and obtain uniqueness results that were not possible in Kreps’ model.
Nonsmooth H ∞ synthesis
Pierre Apkarian,Dominikus Noll +1 more
TL;DR: In this paper, a nonsmooth optimization technique is proposed to solve H∞ synthesis problems under additional structural constraints on the controller, which avoids the use of Lyapunov variables and therefore leads to moderate size optimization programs even for very large systems.
Journal ArticleDOI
Nonsmooth sequential analysis in Asplund spaces
TL;DR: In this article, a generalized differentiation theory for nonsmooth functions and sets with nonconvex boundaries defined in Asplund spaces is developed. But the analysis is restricted to the case of sets with nonsmooted boundaries.