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Non-smooth DC-constrained optimization: constraint qualification and minimizing methodologies

机译：非平滑直流约束优化：约束资格和最小化方法

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摘要

This work concerns the study of a constraint qualification for non-smooth DC-constrained optimization problems, as well as the design and convergence analysis of minimizing algorithms to address the task of computing a stationary/critical point for problems of this class. Specialized algorithms for DC programming approximate the non-convex optimization problem by a sequence of convex subproblems, obtained by linearizing the second components of the involved DC (difference of convex) functions. We propose new approaches that define trial points as inexact solutions of such convex subproblems. This is a property of practical interest that substantially reduces the computational burden to compute a stationary/critical point of non-smooth DC-constrained optimization problems. One variant of the proposed algorithmic patterns is numerically assessed on a DC reformulation of an energy management problem considering a smart-grid controlled by a local actor (follower) and its interaction with a global actor (leader) in the power system.
机译：这项工作涉及对非平滑直流约束优化问题的约束资格的研究，以及最小化算法的设计和收敛性分析，以解决计算该类问题的静止/关键点的任务。用于DC编程的专用算法近似通过线性化涉及的DC的第二组件（凸起）函数的第二组件而获得的凸子问题的序列来近似于凸形优化问题。我们提出了新的方法，将试验点定义为此类凸子问题的不精确解决方案。这是实际兴趣的属性，基本上降低了计算非平滑直流约束优化问题的静止/临界点的计算负担。在考虑由当地actor（从动件）控制的智能电网的能量管理问题的直流重构和其与电力系统中的全球actor（领导者）的交互的能量管理问题的直流重构进行了数值评估了所提出的算法模式的一种变体。

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