A simple canonical form for nonlinear programming problems and its use

TL;DR

This paper introduces a simple canonical form for nonlinear programming problems to facilitate analysis, especially in degenerate cases, and demonstrates its utility by solving an open problem related to constraint qualifications.

Contribution

The paper proposes a novel canonical form for nonlinear programming problems that aids in analyzing degenerate cases and addresses an open problem in constraint qualifications.

Findings

Effective analysis of degenerate nonlinear problems

Resolution of an open problem in constraint qualifications

Simplification of nonlinear programming problem analysis

Abstract

We argue that reducing nonlinear programming problems to a simple canonical form is an effective way to analyze them, specially when the problem is degenerate and the usual linear independence hypothesis does not hold. To illustrate this fact we solve an open problem about constraint qualifications using this simple canonical form.