Ghost Penalties in Nonconvex Constrained Optimization: Diminishing Stepsizes and Iteration Complexity
Ghost Penalties in Nonconvex Constrained Optimization: Diminishing Stepsizes and Iteration Complexity
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DOI：
10.1287/moor.2020.1079
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发表时间：
2017-09
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影响因子：
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通讯作者：
F. Facchinei;V. Kungurtsev;Lorenzo Lampariello;G. Scutari
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文献类型：
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作者：
F. Facchinei;V. Kungurtsev;Lorenzo Lampariello;G. Scutari
考虑非凸约束优化问题，提出了一种新的基于罚函数的收敛分析方法。我们以一种非常规的方式使用了经典的罚函数，因为罚函数只进入收敛的理论分析，而算法本身是无罚的。基于这一思想，我们能够建立几个新的结果，包括第一个关于非凸、约束优化中的递减步长方法的一般分析，显示出收敛于广义固定点，以及序列二次规划类型算法的复杂性研究。
We consider nonconvex constrained optimization problems and propose a new approach to the convergence analysis based on penalty functions. We make use of classical penalty functions in an unconventional way, in that penalty functions only enter in the theoretical analysis of convergence while the algorithm itself is penalty free. Based on this idea, we are able to establish several new results, including the first general analysis for diminishing stepsize methods in nonconvex, constrained optimization, showing convergence to generalized stationary points, and a complexity study for sequential quadratic programming–type algorithms.