Implicit function and tangent cone theorems for singular inclusions and applications to nonlinear programming

TL;DR

This paper extends the implicit function theorem and tangent cone analysis to singular mappings, providing new tools for analyzing solution sets in nonlinear programming and complementarity problems.

Contribution

It introduces generalized implicit function and tangent cone theorems for singular cases, with applications to nonlinear programming and complementarity problems.

Findings

Extended implicit function theorem for singular mappings

Characterized tangent cones to solution sets in singular cases

Applied results to nonlinear programming and complementarity problems

Abstract

The paper is devoted to the implicit function theorem involving singular mappings.We also discuss the form of the tangent cone to the solution set of the generalized equations in singular case and give some examples of applications to nonlinear programming and complementarity problems.