A Scaled Gradient Modified Non-monotone Line Search Method for Constrained Optimization Problems

TL;DR

This paper introduces a scaled gradient non-monotone line search method for constrained optimization, analyzing its convergence and demonstrating superior performance on large-scale fractional and quadratic programming problems.

Contribution

It presents a novel scaled gradient non-monotone line search algorithm with proven convergence properties for strongly quasiconvex functions.

Findings

The method achieves linear convergence rate for strongly quasiconvex problems.

Numerical experiments show improved performance over existing algorithms.

The approach effectively handles large-scale fractional and quadratic programming problems.

Abstract

In this paper, we propose a scaled gradient modified non-monotone line search method for solving constrained minimization problems, and explore several specific properties of this method, namely, its convergence analysis. We discuss the linear convergence rate of the sequence generated by the proposed algorithm to a solution of the constrained minimization problem where the objective function is strongly quasiconvex. We consider numerical examples of large-scale fractional programming and quadratic programming for the function of pseudo convex and strongly quasiconvex and compare the performance of the proposed algorithm with the existing ones for these examples.