Recent Theoretical Advances in Non-Convex Optimization
نویسندگان
چکیده
Motivated by recent increased interest in optimization algorithms for non-convex application to training deep neural networks and other problems data analysis, we give an overview of theoretical results on global performance guarantees optimization. We start with classical arguments showing that general could not be solved efficiently a reasonable time. Then list can find the minimizer exploiting structure problem as much it is possible. Another way deal non-convexity relax goal from finding minimum stationary point or local minimum. For this setting, first present known convergence rates deterministic first-order methods, which are then followed analysis optimal stochastic randomized gradient schemes, methods. After that, discuss quite classes problems, such minimization ?-weakly quasi-convex functions satisfy Polyak–?ojasiewicz condition, still allow obtaining consider higher-order zeroth-order/derivative-free methods their problems.
منابع مشابه
Recent Advances in Combinatorial Optimization
1College of Science, East China Institute of Technology, Nanchang, Jiangxi 330013, China 2Department of Information Management, National Formosa University, Yun-Lin 632, Taiwan 3School of Economics & Management, Tongji University, Shanghai 200092, China 4Laboratoire IBISC, Université d’Evry-Val d’Essone, 40 rue Pelvoux, 91001 Evry, France 5LCOMS EA7306, Université de Lorraine, Ile du Saulcy, 57...
متن کاملRecent Advances in Multiobjective Optimization
Multiobjective (or multicriteria) optimization is a research area with rich history and under heavy investigation within Operations Research and Economics in the last 60 years [1,2]. Its object of study is to investigate solutions to combinatorial optimization problems that are evaluated under several objective functions – typically defined on multidimensional attribute (cost) vectors. In multi...
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ژورنال
عنوان ژورنال: Springer optimization and its applications
سال: 2022
ISSN: ['1931-6828', '1931-6836']
DOI: https://doi.org/10.1007/978-3-031-00832-0_3