Lower-order smoothed objective penalty functions based on filling properties for constrained optimization problems. (3rd June 2022)

• Record Type: Journal Article
• Authors: Tang, Jiahui; Wang, Wei; Xu, Yifan
• Is Part Of: Optimization. Volume 71:Number 6(2022)
• Page Start: 1579
• Page End: 1601
• Publication Date: 2022-06-03
• Subjects: Constrained optimization -- globally optimal solutions -- locally optimal solutions -- smoothed objective penalty functions -- filling properties; 90C30; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2020.1818746
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : In this article, a class of lower-order smoothed objective penalty functions is introduced to find locally optimal points for constrained optimization problems. The exactness of the new penalty functions is studied. Based on the current locally optimal points, a new class of penalty functions based on filling properties is proposed. This new penalty function can be used to find a better locally optimal point. The exactness and filling properties of this penalty function are proved in this paper. To do this, two algorithms are presented to find the locally and globally optimal points. Additionally, their convergence is proved under some mild conditions. Finally, numerical results are included to illustrate the applicability of the local and global optimization algorithms.