Solving Nonlinear Equations with a Convergent Derivative-Free Projection Method Close to a Modified Memoryless Symmetric Rank-one Update

Abstract Derivative-free projection methods have recently gained much interest for solving systems of nonlinear equations. Based on the effectiveness of conjugate gradient methods, and the idea of the projection technique, in this work we develop a new three-term derivative-free projection method for solving nonlinear monotone equations. Specifically, we propose a three-term conjugate gradient based direction that is close to a recently presented modified symmetric rank-one (SR1) method. We prove that the proposed search direction satisfies the descent condition, and further establish the method’s global convergence under appropriate conditions. The efficacy of the method is demonstrated through experiments on some constrained nonlinear equations. Furthermore, the method is used to solve a regularized decentralized logistic regression problem.