Algorithm for solutions of nonlinear equations of strongly monotone type and applications to convex minimization and variational inequality problems

TL;DR

This paper introduces a new algorithm for solving nonlinear equations of strongly monotone type, providing strong convergence results and applications to convex minimization and variational inequality problems across various scientific fields.

Contribution

It presents a novel technique that does not assume the existence of a specific constant, ensuring strong convergence for a class of nonlinear equations of (p, η)-strongly monotone type.

Findings

Established strong convergence results for the proposed algorithm.

Derived solutions for convex minimization and variational inequality problems.

Demonstrated applications in multiple scientific and engineering fields.

Abstract

Real-life problems are governed by equations which are nonlinear in nature. Nonlinear equations occur in modeling problems, such as minimizing costs in industries and minimizing risks in businesses. A technique which does not involve the assumption of existence of a real constant whose calculation is unclear is used to obtain a strong convergence result for nonlinear equations of (p, {\eta})-strongly monotone type, where {\eta} > 0, p > 1. An example is presented for the nonlinear equations of (p, {\eta})-strongly monotone type. As a consequence of the main result, the solutions of convex minimization and variational inequality problems are obtained. This solution has applications in other fields such as engineering, physics, biology, chemistry, economics, and game theory.