论文标题
提起稀疏优化的固定点，并具有互补性约束
Lifted Stationary Points of Sparse Optimization with Complementarity Constraints
论文作者
论文摘要
我们旨在计算具有互补性约束的稀疏优化问题（P0）的固定点。我们定义了一个连续的放松问题（RV），该问题具有相同的全局最小化器和问题的最佳价值（P0）。问题（RV）是一个具有互补性约束（MPCC）和频率差（DC）目标函数的数学程序。我们定义了MPCC的提升平台（RV），并表明它比方向的平稳性弱，但比Clarke Sterarity更强大，以实现局部最优性。此外，我们提出了一种解决（RV）的近似方法和一种增强的拉格朗日方法来解决其子问题，该方法可以放宽（RV）中耐受性的相等性约束。我们证明了我们的算法与MPCC提升的问题点（RV）的收敛性，并将稀疏的优化问题与垂直线性互补性约束一起使用，以证明我们算法在实践中找到稀疏解决方案的效率。
We aim to compute lifted stationary points of a sparse optimization problem (P0) with complementarity constraints. We define a continuous relaxation problem (Rv) that has the same global minimizers and optimal value with problem (P0). Problem (Rv) is a mathematical program with complementarity constraints (MPCC) and a difference-of-convex (DC) objective function. We define MPCC lifted-stationarity of (Rv) and show that it is weaker than directional stationarity, but stronger than Clarke stationarity for local optimality. Moreover, we propose an approximation method to solve (Rv) and an augmented Lagrangian method to solve its subproblem, which relaxes the equality constraint in (Rv) with a tolerance. We prove the convergence of our algorithm to an MPCC lifted-stationary point of problem (Rv) and use a sparse optimization problem with vertical linear complementarity constraints to demonstrate the efficiency of our algorithm on finding sparse solutions in practice.
