A truncated epsilon-subdifferential method for global DC optimization

TL;DR

This paper introduces a novel epsilon-subdifferential method for global difference-of-convex (DC) optimization under box constraints, combining local search with an escaping procedure to find higher-quality solutions efficiently.

Contribution

The paper presents a new global DC optimization method that uses epsilon-subdifferentials and a specialized escaping procedure, improving solution quality over existing local methods.

Findings

The method effectively finds higher-quality solutions in test problems.

It requires reasonable computational effort compared to other global solvers.

The approach outperforms benchmark global optimization solvers in experiments.

Abstract

We consider the difference of convex (DC) optimization problem subject to box constraints. Utilizing epsilon-subdifferentials of DC components of the objective, we develop a new method for finding global solutions to this problem. The method combines a local search approach with a special procedure for escaping non-global solutions by identifying improved initial points for a local search. The method terminates when the solution cannot be improved further. The escaping procedure is designed using subsets of the epsilon-subdifferentials of DC components. We compute the deviation between these subsets and determine epsilon-subgradients, providing this deviation. Using these specific epsilon-subgradients, we formulate a subproblem with a convex objective function. The solution to this subproblem serves as a starting point for a local search. We study the convergence of the conceptual version of the proposed method and discuss its implementation. A large number of academic test problems demonstrate that the method requires reasonable computational effort to find higher-quality solutions than other local DC optimization methods. Additionally, we apply the new method to find global solutions to DC optimization problems and compare its performance with two benchmark global optimization solvers.