论文标题
上c^2目标的非平滑非凸问题的优化算法
An Optimization algorithm for nonsmooth nonconvex problems with upper-C^2 objective
论文作者
论文摘要
提出和分析了针对非c2 c2目标函数的非平滑非凸的优化优化问题的优化算法。上C2是一种弱凹的性能，存在于凸功能差异（DC）函数中，并且在许多应用中自然出现，尤其是某些参数优化问题的解决方案[34，4]，例如随机编程[36]的依次[36]并投影到封闭集中[34]。该算法可以看作是专门用于上C2问题的束方法，并且具有有界算法参数的全球收敛。与常规的捆绑方法相比，所提出的方法既简单又更有效。该算法与顺序二次编程（SQP）方法相似地处理一般平滑约束，并使用线路搜索来确保进步。通过惩罚方法解决了约束线性化的潜在不一致。该算法的功能是通过解决当前电网行业实践中使用的简单上层C2问题和现实世界中最佳功率流问题来证明的。
An optimization algorithm for nonsmooth nonconvex constrained optimization problems with upper-C2 objective functions is proposed and analyzed. Upper-C2 is a weakly concave property that exists in difference of convex (DC) functions and arises naturally in many applications, particularly certain classes of solutions to parametric optimization problems [34, 4], e.g., recourse of stochastic programming [36] and projection into closed sets [34]. The algorithm can be viewed as a bundle method specialized for upper-C2 problems and is globally convergent with bounded algorithm parameters. Compared to conventional bundle methods, the proposed method is both simpler and computationally more efficient. The algorithm handles general smooth constraints similarly to sequential quadratic programming (SQP) methods and uses a line search to ensure progress. The potential inconsistencies from the linearization of the constraints are addressed through a penalty method. The capabilities of the algorithm are demonstrated by solving both simple upper-C2 problems and real-world optimal power flow problems used in current power grid industry practices.
