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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Journal ArticleDOI
The Supporting Hyperplane Method for Unimodal Programming
TL;DR: An algorithm for maximizing a linear unimodal function over a compact convex set X in n-dimensional Euclidian space is proposed, a variant of the cutting-plane method of Cheney and Goldstein and of Kelley, formulated so as to be applicable also to unimmodal integer programs.
Journal ArticleDOI
Asymptotic analysis for penalty and barrier methods in convex and linear programming
TL;DR: This work provides a systematic way to generate penalty and barrier functions in this class of penalty methods for convex programming, and analyzes the existence of primal and dual optimal paths generated by these penalty methods, as well as their convergence to the primal andDual optimal sets.
Journal ArticleDOI
Algorithms with Adaptive Smoothing for Finite Minimax Problems
TL;DR: A new feedback precision-adjustment rule for use with a smoothing technique and standard unconstrained minimization algorithms in the solution of finite minimax problems, which shows that their performance is comparable to or better than that of other algorithms available in the Matlab environment.
Journal ArticleDOI
Approximation procedures based on the method of multipliers
TL;DR: A method for solving certain optimization problems with constraints, nondifferentiabilities, and other ill-conditioning terms in the cost functional by approximating them by well-behaved optimization problems by based on methods of multipliers.
Book ChapterDOI
A smoothing technique for nondifferentiable optimization problems
Aharon Ben-Tal,Marc Teboulle +1 more
TL;DR: In this paper, a smoothing technique for non-differentiable optimization problems is introduced, where the original problem is replaced by an approximate one which is controlled by a smooth parameter.