Journal ArticleDOI
A Branch-and-Bound Approach for Solving a Class of Generalized Semi-infinite Programming Problems
E. Levitin,R. Tichatschke +1 more
TLDR
A branch-and-bound approach is suggested transforming the problem of finding an approximate global minimum of the original nonconvex optimization problem into the solution of a finite number of convex problems.Abstract:
A nonconvex generalized semi-infinite programming problem is considered, involving parametric max-functions in both the objective and the constraints. For a fixed vector of parameters, the values of these parametric max-functions are given as optimal values of convex quadratic programming problems. Assuming that for each parameter the parametric quadratic problems satisfy the strong duality relation, conditions are described ensuring the uniform boundedness of the optimal sets of the dual problems w.r.t. the parameter. Finally a branch-and-bound approach is suggested transforming the problem of finding an approximate global minimum of the original nonconvex optimization problem into the solution of a finite number of convex problems.read more
Citations
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Journal ArticleDOI
A review of recent advances in global optimization
TL;DR: This paper presents an overview of the research progress in deterministic global optimization during the last decade (1998-2008).
Journal ArticleDOI
Solving semi-infinite optimization problems with interior point techniques
Oliver Stein,Georg Still +1 more
TL;DR: A new numerical solution method based on a reformulation of the semi-infinite problem as a Stackelberg game and the use of regularized nonlinear complementarity problem functions to solve lower level optimization problems with convex lower level problems is introduced.
Journal ArticleDOI
Generalized semi-infinite programming: A tutorial
TL;DR: In this article, the authors present an introduction to generalized semi-infinite programming (GSIP) models and present necessary and sufficient first-and second-order optimality conditions where directional differentiability properties of the optimal value function of the lower level problem are used.
Journal ArticleDOI
Generalized semi-infinite programming: Theory and methods
TL;DR: From a theoretical and a practical point of view it is investigated, under which assumptions a GSIP can be transformed into an SIP.
References
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Book
An introduction to optimization
TL;DR: This review discusses mathematics, linear programming, and set--Constrained and Unconstrained Optimization, as well as methods of Proof and Some Notation, and problems with Equality Constraints.
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.