, Volume 99, Issue 2, pp 311327
First online:
Coderivatives in parametric optimization
 Adam B. LevyAffiliated withDepartment of Mathematics, Bowdoin College
 , Boris S. MordukhovichAffiliated withDepartment of Mathematics, Wayne State University
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We consider parametric families of constrained problems in mathematical programming and conduct a local sensitivity analysis for multivalued solution maps. Coderivatives of setvalued mappings are our basic tool to analyze the parametric sensitivity of either stationary points or stationary pointmultiplier 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 pointmultiplier 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 pointmultiplier 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.
Keywords
parametric optimization variational analysis sensitivity Lipschitzian stability generalized differentiation coderivatives Title
 Coderivatives in parametric optimization
 Journal

Mathematical Programming
Volume 99, Issue 2 , pp 311327
 Cover Date
 200403
 DOI
 10.1007/s1010700304520
 Print ISSN
 00255610
 Online ISSN
 14364646
 Publisher
 SpringerVerlag
 Additional Links
 Keywords

 parametric optimization
 variational analysis
 sensitivity
 Lipschitzian stability
 generalized differentiation
 coderivatives
 Industry Sectors
 Authors

 Adam B. Levy ^{(1)}
 Boris S. Mordukhovich ^{(2)}
 Author Affiliations

 1. Department of Mathematics, Bowdoin College, Brunswick, ME, 04011
 2. Department of Mathematics, Wayne State University, Detroit, MI, 48202