Journal ArticleDOI
Second order variational analysis of disjunctive constraint sets and its applications to optimization problems
Vo Duc Thinh,Vo Duc Thinh,Thai Doan Chuong,Thai Doan Chuong,Nguyen Le Hoang Anh,Nguyen Le Hoang Anh +5 more
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TLDR
In this article, the second-order epi-differentiability of the indicator function has been studied for disjunctive constrained problems, including finite union of parabolically derivable and regular sets.Abstract:
In this paper, we examine the properly twice epi-differentiability and compute the second order epi-subderivative of the indicator function to a class of sets including the finite union of parabolically derivable and parabolically regular sets. In this way, we provide no-gap second order optimality conditions for a disjunctive constrained problem. Moreover, we derive applications of our results to some types of disjunctive programs.read more
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A simple proof of second-order sufficient optimality conditions in nonlinear semidefinite optimization
TL;DR: In this article , an elementary proof for the second-order sufficient optimality condition in nonlinear semidefinite optimization is presented, which does not rely on the enhanced theory of secondorder tangents.
References
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Perturbation Analysis of Optimization Problems
TL;DR: It is shown here how the model derived recently in [Bouchut-Boyaval, M3AS (23) 2013] can be modified for flows on rugous topographies varying around an inclined plane.
Journal ArticleDOI
Mathematical Programs with Complementarity Constraints: Stationarity, Optimality, and Sensitivity
Holger Scheel,Stefan Scholtes +1 more
TL;DR: Several stationarity concepts, based on a piecewise smooth formulation, are presented and compared and Fiacco-McCormick type second order optimality conditions and an extension of the stability results of Robinson and Kojima are presented.
Journal ArticleDOI
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.
Journal ArticleDOI
Necessary and sufficient optimality conditions for mathematical programs with equilibrium constraints
TL;DR: A simple proof to the M-stationary condition is given and it is shown that it is sufficient for global or local optimality under some MPEC generalized convexity assumptions.