A nonmonotone spectral projected gradient method for large-scale topology optimization problems

TL;DR

This paper introduces a nonmonotone spectral projected gradient method for large-scale topology optimization, combining adaptive line search and efficient gradient steps to improve convergence and computational performance.

Contribution

It proposes a novel gradient-based algorithm with adaptive nonmonotone line search and cyclic reuse of stepsize, enhancing efficiency and convergence in large-scale topology optimization.

Findings

The method guarantees global convergence.

It requires minimal memory and function evaluations.

Numerical experiments demonstrate high efficiency and feasibility.

Abstract

An efficient gradient-based method to solve the volume constrained topology optimization problems is presented. Each iterate of this algorithm is obtained by the projection of a Barzilai-Borwein step onto the feasible set consisting of box and one linear constraints (volume constraint). To ensure the global convergence, an adaptive nonmonotone line search is performed along the direction that is given by the current and projection point. The adaptive cyclic reuse of the Barzilai-Borwein step is applied as the initial stepsize. The minimum memory requirement, the guaranteed convergence property, and almost only one function and gradient evaluations per iteration make this new method very attractive within common alternative methods to solve large-scale optimal design problems. Efficiency and feasibility of the presented method are supported by numerical experiments.