A derivative-free algorithm for spherically constrained optimization

被引:1
|
作者
Xi, Min [1 ,2 ]
Sun, Wenyu [1 ]
Chen, Yannan [3 ]
Sun, Hailin [1 ]
机构
[1] Nanjing Normal Univ, Sch Math Sci, Jiangsu Key Lab NSLSCS, Nanjing 210023, Peoples R China
[2] Guangdong Univ Foreign Studies, Sch Math & Stat, Guangzhou 510006, Peoples R China
[3] South China Normal Univ, Sch Math Sci, Guangzhou 510631, Peoples R China
基金
中国国家自然科学基金;
关键词
Derivative-free optimization; Spherically constrained optimization; Simple model; Trust-region method; Global convergence; UNCONSTRAINED OPTIMIZATION; EIGENVALUES; CONVERGENCE; LOCATION; VARIANT; MODELS;
D O I
10.1007/s10898-020-00875-2
中图分类号
C93 [管理学]; O22 [运筹学];
学科分类号
070105 ; 12 ; 1201 ; 1202 ; 120202 ;
摘要
Spherically constrained optimization, which minimizes an objective function on a unit sphere, has wide applications in numerical multilinear algebra, signal processing, solid mechanics, etc. In this paper, we consider a certain case that the derivatives of the objective function are unavailable. This case arises frequently in computational science, chemistry, physics, and other enormous areas. To explore the spherical structure of the above problem, we apply the Cayley transform to preserve iterates on the sphere and propose a derivative-free algorithm, which employs a simple model-based trust-region framework. Under mild conditions, global convergence of the proposed algorithm is established. Preliminary numerical experiments illustrate the promising performances of our algorithm.
引用
收藏
页码:841 / 861
页数:21
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