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Sensitivity Analysis in Set-Valued Optimization and Vector Variational Inequalities

2014
Sensitivity analysis, the quantitative analysis of the perturbation map, is of paramount interest in optimization theory and has applications in several branches of pure and applied mathematics. During the last five decades, substantial progress has been made in sensitivity analysis for optimization problems with scalar objectives.
Akhtar A. Khan   +2 more
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Sensitivity analysis for constraint and variational systems by means of set-valued differentiation

Optimization, 1994
In this paper we study general classes of parametric systems arising in optimization and related problems. We provide a local sensitivity analysis of such systems using tools of the generalized differentiation for nonsmooth and set-valued mappings. The main attention is paid to computing the so-called coderivatives of multi-valued solution maps and ...
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Errata to ‘Localized Normal Maps and the Stability of Variational Inclusions’ (Set-Valued Analysis 12 (2004), 259–274)

Set-Valued Analysis, 2006
PROPOSITION 3.1. Assume the hypotheses of Theorem 2.1. Choose w0 2 W0 and take S 1⁄4 U0 fw0g. Define multifunctions X: U0 ! X0 and Z : U0 ! Z0 by requiring that ðu; xÞ belong to the graph of X if and only if ðu;w0; xÞ 2 MS, and that ðu; zÞ belong to the graph of Z if and only if ðu;w0; zÞ 2 NS, where MS and NS are defined by (7).
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