Abstract
We present a new fixed point technique to solve a system of convex equations in several variables. Our approach is based on two powerful algorithmic ideas: operator-splitting and steepest descent direction. The quadratic convergence of the proposed approach is established under some reasonable conditions. Preliminary numerical results are also reported.
Highlights
We present a new fixed point technique to solve a system of convex equations in several variables
System of convex equations is a class of problems that is conceptually close to both constrained and unconstrained optimization and often arise in the applied areas of mathematics, physics, biology, engineering, geophysics, chemistry, and industry
It is noticed that if F x Ax b the system (1) is a linear system of equations and there are a lot of approaches to solve this problem
Summary
System of convex equations is a class of problems that is conceptually close to both constrained and unconstrained optimization and often arise in the applied areas of mathematics, physics, biology, engineering, geophysics, chemistry, and industry. Consider the following system of convex equations. We investigate the global convergence to first-order stationary points of the proposed method and provide the quadratic convergence rate. To show the efficiency of the proposed method in practice, some numerical results are reported. The rest of this paper is organized as follows: In Section 2, we describe the motivation behind the proposed algorithm in the paper together with the algorithm’s structure.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
