Journal ArticleDOI
Extended well-posedness of optimization problems
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In this article, the well-posedness concept introduced in Ref. 1 for global optimization problems with a unique solution is generalized here to problems with many minimizers, under the name of extended wellposedness.Abstract:
The well-posedness concept introduced in Ref. 1 for global optimization problems with a unique solution is generalized here to problems with many minimizers, under the name of extended well-posedness. It is shown that this new property can be characterized by metric criteria, which parallel to some extent those known about generalized Tikhonov well-posedness.read more
Citations
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Convergence and efficiency of subgradient methods for quasiconvex minimization
TL;DR: The general subgradient projection method for minimizing a quasiconvex objective subject to a convex set constraint in a Hilbert space is studied, finding ε-solutions with an efficiency estimate of O(ε-2), thus being optimal in the sense of Nemirovskii.
Journal ArticleDOI
Generalized Levitin--Polyak Well-Posedness in Constrained Optimization
TL;DR: This paper considers Levitin--Polyak-type well-posedness for a general constrained optimization problem and introduces generalized and strongly generalized LevitIn-- Polyak well-posingness.
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Well-Posedness and Scalarization in Vector Optimization
TL;DR: In this paper, the authors study several existing notions of well-posedness for vector optimization problems and separate them into two classes and establish the hierarchical structure of their relationships, and show that under some compactness assumption, quasiconvex problems are well posed.
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Well-posedness of mixed variational inequalities, inclusion problems and fixed point problems
TL;DR: Under suitable conditions, it is proved that the well-posedness of a mixed variational inequality is equivalent to theWell-posednesses of a corresponding inclusion problem.
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Well-posedness by perturbations of mixed variational inequalities in Banach spaces
TL;DR: Some conditions under which the well-posedness by perturbations of a mixed variational inequality is equivalent to the existence and uniqueness of its solution are derived.
References
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Journal ArticleDOI
Nonconvex minimization problems
TL;DR: In this paper, it was shown that the set of continuous linear functionals on a Banach space E which attain their maximum on a prescribed closed convex bounded subset X c E is norm-dense in £ *.
Book
Well-Posed Optimization Problems
Asen L. Dontchev,Tullio Zolezzi +1 more
TL;DR: In this article, Hadamard and tykhonov well-posedness in optimal control and the calculus of variations were defined. But they were not defined in the context of mathematical programming.
Journal ArticleDOI
Well-posedness criteria in optimization with application to the calculus of variations
Journal ArticleDOI
About well-posed optimization problems for functionals in metric spaces
Massimo Furi,Alfonso Vignoli +1 more
TL;DR: A necessary and sufficient condition of correctness of extremal problems for lower semicontinuous functionals defined in metric spaces is given in this paper, which is a necessary condition for extremal problem correctness.