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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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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Journal ArticleDOI
A barrier function method for minimax problems
TL;DR: This paper presents an algorithm based on barrier functions for solving semi-infinite minimax problems which arise in an engineering design setting that is exceptionally robust, and that its performance is comparable, while its structure is simpler than that of current first-order minimax algorithms.
Journal ArticleDOI
Solving min-max problems and linear semi-infinite programs
Shu-Cherng Fang,Soon-Yi Wu +1 more
TL;DR: It is shown that an entropic regularization procedure can provide a smooth approximation F p ( x) that uniformly converges to F ( x ) over X, as p tends to infinity.
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Solving Continuous Min-Max Problems by an Iterative Entropic Regularization Method
Ruey-Lin Sheu,Jen-Yen Lin +1 more
TL;DR: Using a well-known uniform error estimate for entropic regularization, convergence of the overall method is shown while allowing each smoothed problem to be solved inexactly, to solve continuous min-max problems.
Journal ArticleDOI
An Unconstrained Convex Programming Approach to Linear Semi-Infinite Programming
TL;DR: An unconstrained convex programming dual approach for solving a class of linear semi-infinite programming problems is proposed and primal and dual convergence results are established under some basic assumptions.
Journal ArticleDOI
An interior-point method for semi-infinite programming problems
TL;DR: This work examines the generalization of a certain interior-point method, namely the method of analytic centers, to semi-infinite linear programming problems and defines an analytic center and an appropriate norm to examine Newton's method for computing this center.