The Alternating Direction Search Pattern Method for Solving Constrained Nonlinear Optimization Problems

Aifen Feng (), Xiaogai Chang, Youlin Shang and Jingya Fan
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Aifen Feng: School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, China
Xiaogai Chang: School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, China
Youlin Shang: School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, China
Jingya Fan: School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, China

Mathematics, 2023, vol. 11, issue 8, 1-11

Abstract: We adopt the alternating direction search pattern method to solve the equality and inequality constrained nonlinear optimization problems. Firstly, a new augmented Lagrangian function with a nonlinear complementarity function is proposed to transform the original constrained problem into a new unconstrained problem. Under appropriate conditions, it has been proven that there is a 1-1 correspondence between the local and global optimal solutions of the new unconstrained problem and the original constrained problem. In this way, the optimal solution of the original problem can be obtained by solving the new unconstrained optimization problem. Furthermore, based on the characteristics of the new problem, the alternating direction pattern search method was designed and its convergence was demonstrated. Numerical experiments were implemented to illustrate the availability of the new augmented Lagrangian function and the algorithm.

Keywords: nonlinear programming; nonlinear complementarity function; alternating direction search pattern method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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