Journal ArticleDOI
Nonsmooth semi-infinite programming problem using Limiting subdifferentials
TLDR
It is established necessary and sufficient optimality conditions for nonsmooth semi-infinite programming problem using the powerful tool of limiting subdifferentials and Wolfe and Mond-Weir type duals are formulated.Abstract:
In this paper, we establish necessary and sufficient optimality conditions for nonsmooth semi-infinite programming problem using the powerful tool of limiting subdifferentials. We also formulate Wolfe and Mond-Weir type duals for nonsmooth semi-infinite programming problem and establish weak, strong and strict converse duality theorems for semi-infinite programming problem and the corresponding dual problems.read more
Citations
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Journal ArticleDOI
How to solve a semi-infinite optimization problem
TL;DR: This article surveys recent developments in theory and numerical methods for standard and generalized semi-infinite optimization problems, paying particular attention to connections with mathematical programs with complementarity constraints, lower level Wolfe duality, semi-smooth approaches, as well as branch and bound techniques in adaptive convexification procedures.
Journal ArticleDOI
On the stability of solutions for semi-infinite vector optimization problems
TL;DR: Under weak assumptions, sufficient conditions of the Berge-lower semicontinuity and lower Painlev convergence of weak efficient solutions for (SVO) under functional perturbations of both objective functions and constraint sets are established.
Journal ArticleDOI
Optimality Conditions for Approximate Pareto Solutions of a Nonsmooth Vector Optimization Problem with an Infinite Number of Constraints
TL;DR: In this paper, the authors present necessary and sufficient optimality conditions in terms of Clarke subdifferentials for approximate Pareto solutions of a nonsmooth vector optimization problem which has an infinite number of constraints.
Journal ArticleDOI
Optimality Conditions of Approximate Solutions for Nonsmooth Semi-infinite Programming Problems
TL;DR: In this paper, the optimality conditions of approximate solutions for nonsmooth semi-infinite programming problems were studied, and the results obtained in this paper improve the corresponding results of Son et al. (J Optim Theory Appl 141:389-409, 2009).
Journal ArticleDOI
New optimality conditions for nonsmooth control problems
TL;DR: This work considers nonsmooth optimal control problems and provides two new sufficient conditions of optimality, one involving the Lagrange multipliers while the second does not, and shows that under the first new condition all processes satisfying the Pontryagin Maximum Principle are optimal.
References
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Book
Variational Analysis and Generalized Differentiation II
TL;DR: In this article, the authors propose a constrained optimization and equilibrium approach for optimal control of evolution systems in Banach spaces. And they apply this approach to distributed systems in economics applications.
Journal ArticleDOI
Semi-infinite programming: theory, methods, and applications
R. Hettich,K. O. Kortanek +1 more
TL;DR: This paper treats numerical methods based on either discretization or local reduction with the emphasis on the design of superlinearly convergent (SQP-type) methods.
Book
Encyclopedia of Optimization
TL;DR: The second edition of the Encyclopedia of Optimization builds on the success of the former edition with more than 150 completely new entries, designed to ensure that the reference addresses recent areas where optimization theories and techniques have advanced.