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

Ronny Bergmann (), Roland Herzog (), Julián Ortiz López () and Anton Schiela ()
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Ronny Bergmann: Norwegian University of Science and Technology
Roland Herzog: Heidelberg University
Julián Ortiz López: University of Bayreuth
Anton Schiela: University of Bayreuth

Journal of Optimization Theory and Applications, 2022, vol. 195, issue 2, No 9, 596-623

Abstract: Abstract 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.

Keywords: Optimization on manifolds; Manifold-valued constraints; Manifold with corners; First- and second-order optimality conditions; Lagrangian function; 90C30; 90C46; 49Q99; 65K05 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10957-022-02107-x

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