A New Finite-Difference Method for Nonlinear Absolute Value Equations

Peng Wang (), Yujing Zhang and Detong Zhu
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Peng Wang: Key Laboratory of Data Science and Smart Education Ministry of Education, Hainan Normal University, Haikou 570203, China
Yujing Zhang: Key Laboratory of Data Science and Smart Education Ministry of Education, Hainan Normal University, Haikou 570203, China
Detong Zhu: Mathematics and Science College, Shanghai Normal University, Shanghai 200234, China

Mathematics, 2025, vol. 13, issue 5, 1-12

Abstract: In this paper, we propose a new finite-difference method for nonconvex absolute value equations. The nonsmooth unconstrained optimization problem equivalent to the absolute value equations is considered. The finite-difference technique is considered to compose the linear programming subproblems for obtaining the search direction. The algorithm avoids the computation of gradients and Hessian matrices of problems. The new finite-difference parameter correction technique is considered to ensure the monotonic descent of the objective function. The convergence of the algorithm is analyzed, and numerical experiments are reported, indicating the effectiveness by comparison against a state-of-the-art absolute value equations.

Keywords: nonsmooth unconstrained optimization; linear programming methods; approximation gradient; global convergence; multi-directional search (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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