Journal ArticleDOI
Penalty and Smoothing Methods for Convex Semi-Infinite Programming
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This paper introduces a unified framework concerning Remez-type algorithms and integral methods coupled with penalty and smoothing methods that subsumes well-known classical algorithms, but also provides some new methods with interesting properties.Abstract:
In this paper we consider min-max convex semi-infinite programming. To solve these problems we introduce a unified framework concerning Remez-type algorithms and integral methods coupled with penalty and smoothing methods. This framework subsumes well-known classical algorithms, but also provides some new methods with interesting properties. Convergence of the primal and dual sequences are proved under minimal assumptions.read more
Citations
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Journal ArticleDOI
A New Exchange Method for Convex Semi-Infinite Programming
TL;DR: A new dropping-rule is introduced in the proposed exchange algorithm, which only keeps those active constraints with positive Lagrange multipliers and exploits the idea of looking for $\eta$-infeasible indices of the lower level problem as the adding-rule in the algorithm.
Journal ArticleDOI
Recent contributions to linear semi-infinite optimization: an update
TL;DR: The state-of-the-art in the theory of deterministic and uncertain linear semi-infinite optimization is reviewed, some numerical approaches to this type of problems are presented, and a selection of recent applications are described.
Journal ArticleDOI
Stationarity and Regularity of Infinite Collections of Sets
TL;DR: Stationarity criteria developed in the article are applied to proving intersection rules for Fréchet normals to infinite intersections of sets in Asplund spaces.
Journal ArticleDOI
Recent contributions to linear semi-infinite optimization
TL;DR: The state-of-the-art in the theory of deterministic and uncertain linear semi-infinite optimization is reviewed, some numerical approaches to this type of problems are presented, and a selection of recent applications are described.
References
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Book
Asymptotic cones and functions in optimization and variational inequalities
Alfred Auslender,Marc Teboulle +1 more
TL;DR: Convex analysis and set valued maps: A Review and a Review of Set Valued Maps and Set-Valued Maps: Existence and Stability in Optimization Problems, Minimum Monotone Maps and Variational Inequalities as discussed by the authors.
Journal ArticleDOI
Newton's method for convex programming and Tchebycheff approximation
E. W. Cheney,A. A. Goldstein +1 more
TL;DR: The rationale of Newton's method is exploited here in order to develop effective algorithms for solving the following general problem: given a convex continuous function F defined on a closed convex subset K of E,~, obtain a point x of K such that F(x)_<_F(y) for all y in K.
Book ChapterDOI
Numerical Methods for Semi-Infinite Programming: A Survey
Rembert Reemtsen,Stephan Görner +1 more
TL;DR: This paper provides a review of numerical methods for the solution of smooth semi-infinite programming problems and presents fundamental and partly new results on level sets, discretization, and local reduction.
Journal ArticleDOI
A new computational algorithm for functional inequality constrained optimization problems
TL;DR: A computational algorithm is devised for solving a class of functional inequality constrained optimization problems, based on a penalty function, for which a numerical example is solved.
Journal ArticleDOI
A central cutting plane algorithm for the convex programming problem
Jack Elzinga,Thomas G. Moore +1 more
TL;DR: An algorithm is developed for solving the convex programming problem by constructing a cutting plane through the center of a polyhedral approximation to the optimum, which generates a sequence of primal feasible points whose limit points satisfy the Kuhn—Tucker conditions of the problem.