Hybridized Brazilian–Bowein type spectral gradient projection method for constrained nonlinear equations

Abstract

This paper proposes a hybridized Brazilian and Bowein derivative-free spectral gradient projection method for solving systems of convex-constrained nonlinear equations. The method avoids solving any subproblems in each iteration. Global convergence is established under appropriate assumptions on the functions involved. Additionally, numerical experiments are conducted to evaluate the algorithm’s performance, providing evidence of its efficiency compared to similar algorithms from the existing literature. The results demonstrate that the method outperforms some existing approaches in terms of the number of iterations, function evaluations, and time required to obtain a solution based on the examples considered.

Keywords

• Nonexpansive mappings
• Descent direction
• Lipschitz continuity
• Decreasing sequence
• Derivative-free method
• Global convergence