A Path-Based Approach to Constrained Sparse Optimization
提出一种基于路径的方法，用于在稀疏对称集上最小化连续可微函数，无需支持优化预言机且无投影，能实现更严格的最优性条件，并附有数值示例。
.This paper proposes a path-based approach for the minimization of a continuously differentiable function over sparse symmetric sets, which is a hard problem that exhibits a restrictiveness-hierarchy of necessary optimality conditions. To achieve the more restrictive conditions in the hierarchy, state-of-the-art algorithms require a support optimization oracle that must exactly solve the problem in smaller dimensions. The path-based approach developed in this study produces a path-based optimality condition, which is placed well in the restrictiveness-hierarchy, and a method to achieve it that does not require a support optimization oracle and, moreover, is projection-free. In the development process, new results are derived for the regularized linear minimization problem over sparse symmetric sets, which give additional means to identify optimal solutions for convex and concave objective functions. We complement our results with numerical examples.Keywordssparse optimizationnonconvex optimizationpath optimalityconditional gradientMSC codes90C2690C3090C46