In the present paper we propose to rewrite a nonsmooth problem subjected to convex constraints as an unconstrained problem. We show that this novel formulation shares the same global and local minima with the original constrained problem. Moreover, the reformulation can be solved with standard nonsmooth optimization methods if we are able to make projections onto the feasible sets. Numerical evidence shows that the proposed formulation compares favorably against state-of-art approaches. Code can be found at https://github.com/jth3galv/dfppm.

中文翻译：

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具有凸约束的非光滑问题的无参数无约束重构

在本文中，我们建议将受凸约束的非光滑问题重写为无约束问题。我们表明，这种新颖的公式与原始约束问题具有相同的全局和局部最小值。此外，如果我们能够对可行集进行投影，则可以使用标准的非平滑优化方法来解决重构问题。数值证据表明，所提出的配方与最先进的方法相比具有优势。代码可以在 https://github.com/jth3galv/dfppm 找到。