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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.<\/jats:p>","DOI":"10.1007\/s10957-022-02107-x","type":"journal-article","created":{"date-parts":[[2022,9,29]],"date-time":"2022-09-29T18:04:00Z","timestamp":1664474640000},"page":"596-623","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["First- and Second-Order Analysis for Optimization Problems with Manifold-Valued Constraints"],"prefix":"10.1007","volume":"195","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8342-7218","authenticated-orcid":false,"given":"Ronny","family":"Bergmann","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2164-6575","authenticated-orcid":false,"given":"Roland","family":"Herzog","sequence":"additional","affiliation":[]},{"given":"Juli\u00e1n","family":"Ortiz L\u00f3pez","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6959-2951","authenticated-orcid":false,"given":"Anton","family":"Schiela","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,9,29]]},"reference":[{"key":"2107_CR1","doi-asserted-by":"publisher","DOI":"10.1515\/9781400830244","volume-title":"Optimization Algorithms on Matrix Manifolds","author":"PA Absil","year":"2008","unstructured":"Absil, P.A., Mahony, R., Sepulchre, R.: Optimization Algorithms on Matrix Manifolds. 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