First- and Second-Order Analysis for Optimization Problems with Manifold-Valued Constraints
被引:0
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作者:
Ronny Bergmann
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机构:Norwegian University of Science and Technology,Department of Mathematical Sciences
Ronny Bergmann
Roland Herzog
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h-index: 0
机构:Norwegian University of Science and Technology,Department of Mathematical Sciences
Roland Herzog
Julián Ortiz López
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h-index: 0
机构:Norwegian University of Science and Technology,Department of Mathematical Sciences
Julián Ortiz López
Anton Schiela
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h-index: 0
机构:Norwegian University of Science and Technology,Department of Mathematical Sciences
Anton Schiela
机构:
[1] Norwegian University of Science and Technology,Department of Mathematical Sciences
[2] Heidelberg University,Interdisciplinary Center for Scientific Computing
[3] University of Bayreuth,Department of Mathematics
来源:
Journal of Optimization Theory and Applications
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2022年
/
195卷
关键词:
Optimization on manifolds;
Manifold-valued constraints;
Manifold with corners;
First- and second-order optimality conditions;
Lagrangian function;
90C30;
90C46;
49Q99;
65K05;
D O I:
暂无
中图分类号:
学科分类号:
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.