Work

Worst Case Complexity Bounds for Linesearch-Type Derivative-Free Algorithms

Year: 2024

Type: article

Abstract: This paper is devoted to the analysis of worst case complexity bounds for linesearch-type derivative-free algorithms for the minimization of general non-convex smooth functions. We consider a derivative-free algorithm based on a linesearch extrapolation technique. First we prove that it enjoys the same complexity properties which have been proved for pattern and direct search algorithms, namely that the number of iterations and of function evaluations required to drive the norm of the gradient of the objective function below a given threshold $$\epsilon $$ ϵ for the first time is $${{\mathcal {O}}}(\epsilon ^{-2})$$ O ( ϵ - 2 ) in the worst case. This is the first contribution proving worst-case complexity properties for derivative-free linesearch-type algorithms. Then we show that the lineasearch approach used by the described algorithm allows us to guarantee the further property that the number of iterations such that the norm of the gradient is bigger than $$\epsilon $$ ϵ is $$\mathcal{O}(\epsilon ^{-2})$$ O ( ϵ - 2 ) in the worst case.

Source: Journal of Optimization Theory and Applications

DOI: 10.1007/s10957-024-02519-x

Authors: Andrea Brilli, Morteza Kimiaei, Giampaolo Liuzzi, Stefano Lucidi

Institutions: Sapienza University of Rome, University of Vienna

Language: English

Topic: Advanced Optimization Algorithms Research

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funder: Sapienza Università di Roma