Sequential Convex Programming Methods for Solving Nonlinear Optimization Problems with DC constraints

TL;DR

This paper introduces a sequential convex programming algorithm tailored for nonlinear optimization problems with DC constraints, proves its convergence, and demonstrates its effectiveness through numerical tests.

Contribution

It presents a novel SCP algorithm for DC-constrained problems, including a relaxation technique for inconsistent linearizations, and provides convergence analysis.

Findings

The proposed algorithm converges for nonlinear DC problems.

Numerical tests show the algorithm's practical effectiveness.

Relaxation improves handling of inconsistent linearizations.

Abstract

This paper investigates the relation between sequential convex programming (SCP) as, e.g., defined in [24] and DC (difference of two convex functions) programming. We first present an SCP algorithm for solving nonlinear optimization problems with DC constraints and prove its convergence. Then we combine the proposed algorithm with a relaxation technique to handle inconsistent linearizations. Numerical tests are performed to investigate the behaviour of the class of algorithms.