Second-Order Subdifferential Optimality Conditions in Nonsmooth Optimization
arxiv(2023)
Abstract
The paper is devoted to deriving novel second-order necessary and sufficient
optimality conditions for local minimizers in rather general classes of
nonsmooth unconstrained and constrained optimization problems in
finite-dimensional spaces. The established conditions are expressed in terms of
second-order subdifferentials of lower semicontinuous functions and mainly
concern prox-regular objectives that cover a large territory in nonsmooth
optimization and its applications. Our tools are based on the machinery of
variational analysis and second-order generalized differentiation. The obtained
general results are applied to problems of nonlinear programming, where the
derived second-order optimality conditions are new even for problems with twice
continuously differential data, being expressed there in terms of the classical
Hessian matrices.
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