Coderivatives in parametric optimization

We consider parametric families of constrained problems in mathematical programming and conduct a local sensitivity analysis for multivalued solution maps. Coderivatives of set-valued mappings are our basic tool to analyze the parametric sensitivity of either stationary points or stationary point-mu...

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Vydané v:Mathematical programming Ročník 99; číslo 2; s. 311 - 327
Hlavní autori: Levy, Adam B., Mordukhovich, Boris S.
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Heidelberg Springer 01.03.2004
Springer Nature B.V
Predmet:
Applied sciences
Digital Object Identifier
Estimates
Exact sciences and technology
Mathematical functions
Mathematical programming
Operational research and scientific management
Operational research. Management science
Optimization
Optimization algorithms
Sensitivity analysis
Studies
Sensitivity analysis
Multivalued function
Parametric sensitivity
Parametric programming
variational analysis
Lipschitzian stability
Optimization
parametric optimization
coderivatives
sensitivity
Differentiation
Mathematical programming
generalized differentiation
ISSN:0025-5610, 1436-4646
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Popis
Shrnutí:We consider parametric families of constrained problems in mathematical programming and conduct a local sensitivity analysis for multivalued solution maps. Coderivatives of set-valued mappings are our basic tool to analyze the parametric sensitivity of either stationary points or stationary point-multiplier pairs associated with parameterized optimization problems. An implicit mapping theorem for coderivatives is one key to this analysis for either of these objects, and in addition, a partial coderivative rule is essential for the analysis of stationary points. We develop general results along both of these lines and apply them to study the parametric sensitivity of stationary points alone, as well as stationary point-multiplier pairs. Estimates are computed for the coderivative of the stationary point multifunction associated with a general parametric optimization model, and these estimates are refined and augmented by estimates for the coderivative of the stationary point-multiplier multifunction in the case when the constraints are representable in a special composite form. When combined with existing coderivative formulas, our estimates are entirely computable in terms of the original data of the problem. [PUBLICATION ABSTRACT]
Bibliografia:SourceType-Scholarly Journals-1
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content type line 14
ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-003-0452-0