Concepts and techniques of optimization on the sphere

被引：41
作者：
Ferreira, O. P. [1 ]
Iusem, A. N. [2 ]
Nemeth, S. Z. [3 ]
机构：
[1] IME UFG, BR-74001970 Goiania, Go, Brazil
[2] Inst Matematica Pura & Aplicada, BR-22460320 Rio De Janeiro, RJ, Brazil
[3] Univ Birmingham, Sch Math, Birmingham B15 2TT, W Midlands, England
来源：
TOP | 2014年 / 22卷 / 03期
关键词：
Sphere; Convex function in the sphere; Spheric constrained optimization; Variational problem; Monotone vector fields; RIEMANNIAN-MANIFOLDS; FACILITY LOCATION; VARIATIONAL-INEQUALITIES; VECTOR-FIELDS; CONVEX CONE; ALGORITHM; TENSOR; APPROXIMATION; CONVERGENCE; MINIMAX;
D O I：
10.1007/s11750-014-0322-3
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：
In this paper some concepts and techniques of Mathematical Programming are extended in an intrinsic way from the Euclidean space to the sphere. In particular, the notion of convex functions, variational problem and monotone vector fields are extended to the sphere and several characterizations of these notions are shown. As an application of the convexity concept, necessary and sufficient optimality conditions for constrained convex optimization problems on the sphere are derived.
引用
收藏
页码：1148 / 1170
页数：23
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