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Optimization and nonsmooth analysis
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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
On stochastic programming. II: Dynamic problems under risk
TL;DR: Recent work on dynamic stochastic programming problems and their applications is surveyed, including new results on the measurability and interpretation-in terms of the expected value of perfect information (EVPI)-of the dual multiplier processes corresponding to these problems.
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First order optimality conditions for mathematical programs with semidefinite cone complementarity constraints
Chao Ding,Defeng Sun,Jane J. Ye +2 more
TL;DR: This paper derives explicit formulas for the proximal and limiting normal cone of the graph of the normal cone to the positive semidefinite cone and gives constraint qualifications under which a local solution of SDCMPCC is a S-, M- and C-stationary point.
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Weak Sharp Minima: Characterizations and Sufficient Conditions
Marcin Studniarski,Doug E. Ward +1 more
TL;DR: The problem of identifying weak sharp minima of order m, an important class of (possibly) nonisolated minima, is investigated, and some characterizations of weak sharp minimality are obtained.
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Optimization and Pseudospectra, with Applications to Robust Stability
TL;DR: It is shown that, in a neighborhood of any nonderogatory matrix, the pseudospectral abscissa is a nonsmooth but locally Lipschitz and subdifferentially regular function for sufficiently small $\epsilon$; in fact, it can be expressed locally as the maximum of a finite number of smooth functions.
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Approximations and Metric Regularity in Mathematical Programming in Banach Space
Abderrahim Jourani,L. Thibault +1 more
TL;DR: Verifiable conditions ensuring the important notion of metric regularity for general nondifferentiable programming problems in Banach spaces are established and used to obtain Lagrange-Kuhn-Tucker multipliers for minimization problems with infinitely many inequality and equality constraints.