First- and Second-Order Analysis for Optimization Problems with Manifold-Valued Constraints

被引：2

作者：

Bergmann, Ronny ^{[1
]}

Herzog, Roland ^{[2
]}

Lopez, Julian Ortiz ^{[3
]}

Schiela, Anton ^{[3
]}

机构：

[1] Norwegian Univ Sci & Technol, Dept Math Sci, N-7491 Trondheim, Norway

[2] Heidelberg Univ, Interdisciplinary Ctr Sci Comp, D-69120 Heidelberg, Germany

[3] Univ Bayreuth, Dept Math, D-95440 Bayreuth, Germany

来源：

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS | 2022年 / 195卷 / 02期

关键词：

Optimization on manifolds; Manifold-valued constraints; Manifold with corners; First- and second-order optimality conditions; Lagrangian function;

D O I：

10.1007/s10957-022-02107-x

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：

We consider optimization problems with manifold-valued constraints. These generalize classical equality and inequality constraints to a setting in which both the domain and the codomain of the constraint mapping are smooth manifolds. We model the feasible set as the preimage of a submanifold with corners of the codomain. The latter is a subset which corresponds to a convex cone locally in suitable charts. We study first- and second-order optimality conditions for this class of problems. We also show the invariance of the relevant quantities with respect to local representations of the problem.

引用

页码：596 / 623

页数：28

共 18 条

[1]

Absil PA, 2008, OPTIMIZATION ALGORITHMS ON MATRIX MANIFOLDS, P1

[2]

[Anonymous], 2007, Introduction to the theory of nonlinear optimization

[3] INTRINSIC FORMULATION OF KKT CONDITIONS AND CONSTRAINT QUALIFICATIONS ON SMOOTH MANIFOLDS [J].