Second-Order Variational Analysis of Parametric Constraint and Variational Systems

TL;DR

This paper develops a second-order variational analysis framework for parametric constraint systems, deriving formulas for normal cone mappings and stability conditions in nonpolyhedral conic programming.

Contribution

It introduces a second-order analysis approach for normal cone mappings in parametric systems under weak regularity conditions, extending existing theory.

Findings

Derived explicit formulas for the graphical derivative of the normal cone mapping.

Established conditions for the stability property of isolated calmness.

Applied results to solution stability in parametric variational systems.

Abstract

This paper is devoted to the generalized differential study of the normal cone mappings associated with a large class of parametric constraint systems (PCS) that appear, in particular, in nonpolyhedral conic programming. Conducting a local second-order analysis of such systems, we focus on computing the (primal-dual) graphical derivative of the normal cone mapping under the $C^2$-cone reducibility of the constraint set together with the fairly weak metric subregularity constraint qualification and its uniform parametric counterpart known as Robinson stability. The obtained precise formulas for computing the underlying second-order object are applied to the derivation of comprehensive conditions ensuring the important stability property of isolated calmness for solution maps to parametric variational systems associated with the given PCS.