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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Comparative study of RPSALG algorithm for convex semi-infinite programming
TL;DR: This paper implements different variants of RPSALG which are compared with the unique publicly available SIP solver, NSIPS, on a battery of test problems.
Journal ArticleDOI
Stationarity and Regularity of Infinite Collections of Sets. Applications to Infinitely Constrained Optimization
TL;DR: This article considers several settings of optimization problems which involve (explicitly or implicitly) infinite collections of sets and deduce for them necessary conditions characterizing stationarity in terms of dual space elements—normals and/or subdifferentials.
Journal ArticleDOI
Subsmooth semi-infinite and infinite optimization problems
Xi Yin Zheng,Kung Fu Ng +1 more
TL;DR: This work considers subsmoothness for a function family and provides formulas of the subdifferential of the pointwise supremum of a family of subsm smooth functions and several dual and primal characterizations for a point to be a sharp minimum or a weak sharp minimum for optimization problems.
Posted Content
Model-free bounds for multi-asset options using option-implied information and their exact computation
TL;DR: A fundamental theorem of asset pricing is provided for this market model, as well as a superhedging duality result, that allows to transform the abstract maximization problem over probability measures into a more tractable minimization problems over vectors, subject to certain constraints.
Journal ArticleDOI
An exchange method with refined subproblems for convex semi-infinite programming problems
TL;DR: This paper proposes a new exchange method for solving convex semi-infinite programming problems (SIPs), in which the traditional finite subproblems are refined by the quadratic approximation, and establishes the global convergence property of the proposed algorithm.
References
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Journal ArticleDOI
Smooth minimization of non-smooth functions
TL;DR: A new approach for constructing efficient schemes for non-smooth convex optimization is proposed, based on a special smoothing technique, which can be applied to functions with explicit max-structure, and can be considered as an alternative to black-box minimization.
Book
Perturbation Analysis of Optimization Problems
TL;DR: It is shown here how the model derived recently in [Bouchut-Boyaval, M3AS (23) 2013] can be modified for flows on rugous topographies varying around an inclined plane.
Journal ArticleDOI
A class of smoothing functions for nonlinear and mixed complementarity problems
Chunhui Chen,Olvi L. Mangasarian +1 more
TL;DR: A class of parametric smooth functions that approximate the fundamental plus function, (x)+=max{0, x}, by twice integrating a probability density function leads to classes of smooth parametric nonlinear equation approximations of nonlinear and mixed complementarity problems (NCPs and MCPs).