First- and Second-Order Analysis for Optimization Problems with Manifold-Valued Constraints
研究了约束映射的域和余域均为光滑流形时的优化问题，将可行集建模为余域中带角子流形的原像，并给出了该类问题的一阶和二阶最优性条件。
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.