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Partial Second-Order Subdifferentials in Variational Analysis and Optimization

Boris Mordukhovich(boris***at***math.wayne.edu)
Nguyen Mau Nam(mau.nam.nguyen***at***pdx.edu)
Nguyen Thi Yen Nhi(nhi***at***math.wayne.edu)

Abstract: This paper presents a systematic study of partial second-order subdifferentials for extended-real-valued functions, which have already been applied to important issues of variational analysis and constrained optimization in finite-dimensional spaces. The main results concern developing extended calculus rules for these second-order constructions in both finite-dimensional and infinite-dimensional frameworks. We also provide new applications of partial second-order subdifferentials to Lipschitzian stability of stationary point mappings in parametric constrained optimization and discuss some other applications.

Keywords: Variational analysis, parametric constrained optimization, generalized differentiation, coderivatives, second-order subdifferentials, stability, stationary point mappings

Category 1: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Citation:

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Entry Submitted: 12/26/2012
Entry Accepted: 12/26/2012
Entry Last Modified: 12/26/2012

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