Minimization of sub-topical functions over a simplex

Iranian Journal of Numerical Analysis and Optimization

مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 06 آبان 1402

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2023.83361.1290

نویسندگان

Mohammad Hossein Daryaei^* ؛ Mohammad Ali Yaghoobi

Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran.

چکیده

This article investigates a particular version of the cutting angle method for finding the global minimizer of sub-topical (increasing and plus sub-homogeneous) functions over a simplex. The cutting angle method is a powerful technique that can solve a wide range of global optimization problems based on abstract convexity. This method was proposed in 1999 as a method of global Lipschitz optimization and is a deterministic global optimization technique that involves constructing a sequence of lower approximations to an objective function. The algorithm in this paper is based on the abstract convexity of sub-topical functions. Furthermore, we discuss the proof of convergence of the algorithm and provide results from numerical experiments.

کلیدواژه‌ها

Abstract convexity؛ Global optimization؛ Sub-topical functions؛ Cutting angle method