标题： 一种改进的精确惩罚方法用于一般约束的$\ell_0$-稀疏优化问题 显示英文标题

标题： A modified exact penalty approach for general constrained $\ell_0$-sparse optimization problems

摘要： 我们考虑一类带有目标函数中额外$\ell_0$-稀疏项的约束优化问题。 基于对此困难$\ell_0$-项的最新重新表述，我们考虑一种非光滑惩罚方法，该方法与作者之前的工件不同之处在于它可以直接应用于不一定包含非负性约束的问题。 这避免了将自由变量拆分为其正部分和负部分，减少了维度，并充分利用了给定$\ell_0$-稀疏优化问题与其重新表述之间局部极小值和全局极小值的一一对应关系。 该惩罚方法在极小值和稳定点方面被证明是精确的。 由于惩罚函数是（轻微）非光滑的，我们还介绍了用于求解惩罚公式中出现的子问题的实际技术。 最后，提供了大量数值测试的结果。 显示英文摘要

摘要： We consider a general class of constrained optimization problems with an additional $\ell_0$- sparsity term in the objective function. Based on a recent reformulation of this difficult $\ell_0$-term, we consider a nonsmooth penalty approach which differs from the authors previous work by the fact that it can be directly applied to problems which do not necessarily contain nonnegativity constraints. This avoids a splitting of free variables into their positive and negative parts, reduces the dimension and fully exploits the one-to-one correspondence between local and global minima of the given $\ell_0$-sparse optimization problem and its reformulation. The penalty approach is shown to be exact in terms of minima and stationary points. Since the penalty function is (mildly) nonsmooth, we also present practical techniques for the solution of the subproblems arising within the penalty formulation. Finally, the results of an extensive numerical testing are provided.