Sequential optimality conditions for cardinality-constrained optimization problems with applications
针对基数约束优化问题，提出了一种基于连续重构的序列最优性条件，该条件在局部极小点处成立且无需约束规范，并应用于改进正则化方法和乘子罚函数法的收敛性分析。
Abstract Recently, a new approach to tackle cardinality-constrained optimization problems based on a continuous reformulation of the problem was proposed. Following this approach, we derive a problem-tailored sequential optimality condition, which is satisfied at every local minimizer without requiring any constraint qualification. We relate this condition to an existing M-type stationary concept by introducing a weak sequential constraint qualification based on a cone-continuity property. Finally, we present two algorithmic applications: We improve existing results for a known regularization method by proving that it generates limit points satisfying the aforementioned optimality conditions even if the subproblems are only solved inexactly. And we show that, under a suitable Kurdyka–Łojasiewicz-type assumption, any limit point of a standard (safeguarded) multiplier penalty method applied directly to the reformulated problem also satisfies the optimality condition. These results are stronger than corresponding ones known for the related class of mathematical programs with complementarity constraints.