A Julia implementation of Algorithm NCL for constrained optimization

TL;DR

This paper presents a Julia implementation of Algorithm NCL, a method for smooth constrained optimization that handles problems without LICQ, demonstrating its effectiveness on various test problems.

Contribution

The paper introduces a Julia-based implementation of Algorithm NCL, capable of solving general constrained problems including those lacking LICQ, and provides numerical results on diverse test cases.

Findings

Effective on problems without LICQ

Performs well on tax policy models and nonlinear least-squares

Compatible with IPOPT and KNITRO solvers

Abstract

Algorithm NCL is designed for general smooth optimization problems where first and second derivatives are available, including problems whose constraints may not be linearly independent at a solution (i.e., do not satisfy the LICQ). It is equivalent to the LANCELOT augmented Lagrangian method, reformulated as a short sequence of nonlinearly constrained subproblems that can be solved efficiently by IPOPT and KNITRO, with warm starts on each subproblem. We give numerical results from a Julia implementation of Algorithm NCL on tax policy models that do not satisfy the LICQ, and on nonlinear least-squares problems and general problems from the CUTEst test set.