A pattern search bound constrained optimization method with a nonmonotone line search strategy

TL;DR

This paper introduces a derivative-free pattern search algorithm for bound constrained optimization that uses a nonmonotone line search, demonstrating strong convergence and competitive performance through numerical experiments.

Contribution

It proposes a novel pattern search method with a nonmonotone line search for bound constrained problems, enhancing global convergence analysis without derivatives.

Findings

The new algorithm shows strong global convergence properties.

Numerical experiments demonstrate competitive performance against existing methods.

The method effectively handles bound constraints using coordinate directions.

Abstract

A new pattern search method for bound constrained optimization is introduced. The proposed algorithm employs the coordinate directions, in a suitable way, with a nonmonotone line search for accepting the new iterate, without using derivatives of the objective function. The main global convergence results are strongly based on the relationship between the step length and a stationarity measure. Several numerical experiments are performed using a well known set of test problems. Other line search strategies were tested and compared with the new algorithm.