Cardinality-Constrained Multi-objective Optimization: Novel Optimality Conditions and Algorithms
研究了变量向量带稀疏约束的多目标优化问题，定义了L-平稳性概念，提出了两种新算法（迭代硬阈值法和两阶段法），并证明了其收敛到Pareto最优点的理论性质。
Abstract In this paper, we consider multi-objective optimization problems with a sparsity constraint on the vector of variables. For this class of problems, inspired by the homonymous necessary optimality condition for sparse single-objective optimization, we define the concept of L -stationarity and we analyze its relationships with other existing conditions and Pareto optimality concepts. We then propose two novel algorithmic approaches: the first one is an iterative hard thresholding method aiming to find a single L -stationary solution, while the second one is a two-stage algorithm designed to construct an approximation of the whole Pareto front. Both methods are characterized by theoretical properties of convergence to points satisfying necessary conditions for Pareto optimality. Moreover, we report numerical results establishing the practical effectiveness of the proposed methodologies.