2022/01/28 by Mohamed Tarek, Tarek, Mohamed, Yijiang Huang +1
Computer Science · Mathematics · #Advanced Multi-Objective Optimization Algorithms #Computation (stat.CO) #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning and Algorithms #Optimization and Control (math.OC) #cs.LG #math.OC #stat.CO
paper · pdf · doi:10.48550/arxiv.2201.11926
arxiv created 2022/01/28 · openalex publication_date 2022/01/28 · arxiv updated 2022/01/31 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28
Non-convex optimization problems have multiple local optimal solutions. Non-convex optimization problems are commonly found in numerous applications. One of the methods recently proposed to efficiently explore multiple local optimal solutions without random re-initialization relies on the concept of deflation. In this paper, different ways to use deflation in non-convex optimization and nonlinear system solving are discussed. A simple, general and novel deflation constraint is proposed to enable the use of deflation together with existing nonlinear programming solvers or nonlinear system solvers. The connection between the proposed deflation constraint and a minimum distance constraint is presented. Additionally, a number of variations of deflation constraints and their limitations are discussed. Finally, a number of applications of the proposed methodology in the fields of approximate Bayesian inference and topology optimization are presented.