Exact formulas for the proximal/regular/limiting normal cone of the second-order cone complementarity set

TL;DR

This paper derives explicit formulas for the proximal, regular, and limiting normal cones of the second-order cone complementarity set, which are crucial for optimality conditions and stability analysis in related mathematical programs.

Contribution

It provides the first explicit formulas for these normal cones of the second-order cone complementarity set, advancing theoretical tools for optimization problems.

Findings

Explicit formulas for the proximal normal cone

Explicit formulas for the regular normal cone

Explicit formulas for the limiting normal cone

Abstract

The proximal, regular and limiting normal cones to the second-order cone complementarity set play important roles in studying mathematical programs with second-order cone complementarity constraints, second-order cone programs, and the second-order cone complementarity problems. It is needed in the first-order optimality conditions for mathematical programs with second-order cone complementarity constraint, the second-order subdifferential criteria in characterizing the full stability for second-order cone programs and second-order cone complementarity problems, as well as in the characterizing the pseudo-Lipschitz continuity of the solution mapping to parametric second-order cone complementarity problems. In this paper we establish explicit formulas for the proximal, regular, and limiting normal cone of the second-order cone complementarity set.