Characterization of essential stability in lower pseudocontinuous optimization problems

In this work, our aim is to obtain conditions to assure polynomial approximation in Hilbert spaces L 2 ( μ ) , with μ a compactly supported measure in the complex plane, in terms of properties of the associated moment matrix with the measure μ . To do it, in the more general context of Hermitian positive semidefinite matrices, we introduce two indexes, γ ( M ) and λ ( M ) , associated with different optimization problems concerning theses matrices. Our main result is a characterization of density of polynomials in the case of measures supported on Jordan curves with non-empty interior using the index γ and other specific index related to it. Moreover, we provide a new point of view of bounded point evaluations associated with a measure in terms of the index γ that will allow us to give an alternative proof of Thomson’s theorem, by using these matrix indexes. We point out that our techniques are based in matrix algebra tools in the framework of Hermitian positive definite matrices and in the computation of certain indexes related to some optimization problems for infinite matrices.

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Characterization of semicontinuity of solutions to abstract optimization problems

Numerical Functional Analysis and Optimization ◽

10.1080/01630568708816256 ◽

1987 ◽

Vol 9 (7-8) ◽

pp. 685-708

Author(s):

Ewa Bednarczuk

Keyword(s):

Optimization Problems ◽

Abstract Optimization

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HYBRID SEARCH STRATEGIES FOR HETEROGENEOUS SEARCH SPACES

International Journal of Artificial Intelligence Tools ◽

10.1142/s0218213000000057 ◽

2000 ◽

Vol 09 (01) ◽

pp. 45-57 ◽

Cited By ~ 1

Author(s):

CARLA GOMES ◽

BART SELMAN

Keyword(s):

Operations Research ◽

Resource Constraints ◽

Optimization Problems ◽

Search Strategies ◽

Mixed Integer ◽

Hybrid Search ◽

Search Spaces ◽

Probabilistic Information ◽

Numeric Information

Recently, there has been much interest in enhancing purely combinatorial formalisms with numerical information. For example, planning formalisms can be enriched by taking resource constraints and probabilistic information into account. The Mixed Integer Programming (MIP) paradigm from operations research provides a natural tool for solving optimization problems that combine such numeric and non-numeric information. The MIP approach relies heavily on linear program relaxations and branch-and-bound search. This is in contrast with depth-first or iterative deepening strategies generally used in artificial intelligence. We provide a detailed characterization of the structure of the underlying search spaces as explored by these search strategies. Our analysis shows that much can be gained by combining different search strategies for solving hard MIP problems, thereby leveraging each strategy's strength in terms of the combinatorial and numeric information.

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Characterization of Approximate Solutions of Vector Optimization Problems with a Variable Order Structure

Journal of Optimization Theory and Applications ◽

10.1007/s10957-014-0535-5 ◽

2014 ◽

Vol 162 (2) ◽

pp. 605-632 ◽

Cited By ~ 12

Author(s):

Behnam Soleimani

Keyword(s):

Vector Optimization ◽

Optimization Problems ◽

Approximate Solutions ◽

Vector Optimization Problems ◽

Order Structure ◽

Variable Order

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ϵ-Henig Saddle Points and Duality of Set-Valued Optimization Problems in Real Linear Spaces

The Scientific World JOURNAL ◽

10.1155/2013/403642 ◽

2013 ◽

Vol 2013 ◽

pp. 1-6

Author(s):

Zhi-Ang Zhou

Keyword(s):

Saddle Point ◽

Optimization Problem ◽

Optimization Problems ◽

Saddle Points ◽

Linear Spaces ◽

Equivalent Characterization ◽

Generalized Cone Subconvexlikeness ◽

Real Linear ◽

The Relationship

We studyϵ-Henig saddle points and duality of set-valued optimization problems in the setting of real linear spaces. Firstly, an equivalent characterization ofϵ-Henig saddle point of the Lagrangian set-valued map is obtained. Secondly, under the assumption of the generalized cone subconvexlikeness of set-valued maps, the relationship between theϵ-Henig saddle point of the Lagrangian set-valued map and theϵ-Henig properly efficient element of the set-valued optimization problem is presented. Finally, some duality theorems are given.

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