In many engineering applications, it is necessary to minimize smooth functions plus penalty (or regularization) terms that violate smoothness and convexity. Specific algorithms for this type of problems are available in recent literature. Here, a smooth reformulation is analyzed and equivalence with the original problem is proved both from the points of view of global and local optimization. Moreover, for the cases in which the objective function is much more expensive than the constraints, model-intensive algorithms, accompanied by their convergence and complexity theories, are introduced. Finally, numerical experiments are presented.

中文翻译：

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关于非凸正则化的约束优化

在许多工程应用中，必须最小化平滑函数以及违反平滑度和凸度的罚金（或正则化）项。在最近的文献中可以找到针对这类问题的特定算法。在此，从全局和局部优化的角度分析了平滑的重构，并证明了与原始问题的等效性。此外，对于目标函数比约束条件昂贵得多的情况，引入了模型密集型算法以及它们的收敛性和复杂性理论。最后，给出了数值实验。