Can optimization techniques solve complex mathematical challenges? This paper explores the convergence analysis of the gradient projection method on the sphere for a closed spherically convex set. The research applies this algorithm to discuss copositivity of operators with respect to cones and analyze the solvability of nonlinear cone-complementarity problems. This paper presents the first numerical method related to the copositivity of operators with respect to the positive semidefinite cone. This approach uses a constant step-size. The method offers a novel framework for addressing complex optimization problems with constraints. Numerical results concerning the copositivity of operators are also provided. By developing and testing this method, the research contributes to advancements in optimization techniques and their applications in diverse fields.
As a contribution to the Journal of Global Optimization, this article enhances the journal's coverage of optimization methodologies and their applications. The focus on the gradient projection method and its use in solving complementarity problems is directly relevant to the journal's audience of researchers and practitioners in optimization.