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

Author

Listed:
  • Ronny Bergmann

    (Norwegian University of Science and Technology)

  • Roland Herzog

    (Heidelberg University)

  • Julián Ortiz López

    (University of Bayreuth)

  • Anton Schiela

    (University of Bayreuth)

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.

Suggested Citation

  • Ronny Bergmann & Roland Herzog & Julián Ortiz López & Anton Schiela, 2022. "First- and Second-Order Analysis for Optimization Problems with Manifold-Valued Constraints," Journal of Optimization Theory and Applications, Springer, vol. 195(2), pages 596-623, November.
    • Handle: RePEc:spr:joptap:v:195:y:2022:i:2:d:10.1007_s10957-022-02107-x
    DOI: 10.1007/s10957-022-02107-x
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