An Augmented Lagrangian Method for Cardinality-Constrained Optimization Problems
将基数约束优化问题转化为带正交约束的连续非线性问题，并用标准增广拉格朗日方法求解，证明全局收敛性，数值实验显示其优于正则化方法。
Abstract A reformulation of cardinality-constrained optimization problems into continuous nonlinear optimization problems with an orthogonality-type constraint has gained some popularity during the last few years. Due to the special structure of the constraints, the reformulation violates many standard assumptions and therefore is often solved using specialized algorithms. In contrast to this, we investigate the viability of using a standard safeguarded multiplier penalty method without any problem-tailored modifications to solve the reformulated problem. We prove global convergence towards an (essentially strongly) stationary point under a suitable problem-tailored quasinormality constraint qualification. Numerical experiments illustrating the performance of the method in comparison to regularization-based approaches are provided.