论文标题
通过多项式扰动的频率约束优化的稳定近似
Robust approximation of chance constrained optimization with polynomial perturbation
论文作者
论文摘要
本文提出了一种稳健的近似方法，用于解决多项式的频率约束优化（CCO）。假设CCO是用个人机会约束定义的，该限制是决策变量中的仿射。我们通过在不确定性集上使用强大的约束来替换机会约束来构建强大的近似。当目标函数是线性或SOS-convex时，可稳定的近似可以等效地转换为线性圆锥优化。提出了半决赛弛豫算法，以求解全球的这些线性圆锥变换，并研究其收敛性。我们还引入了一种启发式方法，以找到有效的不确定性集，以使稳健近似的优化者对于原始问题是可行的。进行数值实验以显示我们方法的效率。
This paper proposes a robust approximation method for solving chance constrained optimization (CCO) of polynomials. Assume the CCO is defined with an individual chance constraint that is affine in the decision variables. We construct a robust approximation by replacing the chance constraint with a robust constraint over an uncertainty set. When the objective function is linear or SOS-convex, the robust approximation can be equivalently transformed into linear conic optimization. Semidefinite relaxation algorithms are proposed to solve these linear conic transformations globally and their convergent properties are studied. We also introduce a heuristic method to find efficient uncertainty sets such that optimizers of the robust approximation are feasible to the original problem. Numerical experiments are given to show the efficiency of our method.
