论文标题
非convex和非平滑方法的仿射机会约束随机程序
Nonconvex and Nonsmooth Approaches for Affine Chance-Constrained Stochastic Programs
论文作者
论文摘要
偶然受限的程序（CCP）构成了一类艰难的随机程序，因为即使使用简单的线性随机函数，其可能的非不同性和非凸性也是如此。解决CCP的现有方法主要处理概率函数中的凸随机功能。在本文中，我们考虑了文献中常见研究的偶然限制类别的两个概括。一种概括涉及分离的非convex功能事件的概率，而另一个概括涉及所得概率的混合贴仿生组合。我们共同为这些广义机会限制了术语仿射机会约束（ACC）系统。我们对这种ACC系统的拟议处理涉及几个个别已知的思想的融合：（a）指标函数的参数化上和下近似值在预期的概率提出时； （b）基于期望运算符的外部（即固定）与内部（即顺序）采样的近似； （c）限制惩罚是对可行性的放松； （d）通过替代的非概念性和非差异性的凸化。这些技术的整合以解决不同程度的实用性和计算努力的仿射机会约束随机程序（ACC-SP）的整合是本文的主要贡献。
Chance-constrained programs (CCPs) constitute a difficult class of stochastic programs due to its possible nondifferentiability and nonconvexity even with simple linear random functionals. Existing approaches for solving the CCPs mainly deal with convex random functionals within the probability function. In the present paper, we consider two generalizations of the class of chance constraints commonly studied in the literature; one generalization involves probabilities of disjunctive nonconvex functional events and the other generalization involves mixed-signed affine combinations of the resulting probabilities; together, we coin the term affine chance constraint (ACC) system for these generalized chance constraints. Our proposed treatment of such an ACC system involves the fusion of several individually known ideas: (a) parameterized upper and lower approximations of the indicator function in the expectation formulation of probability; (b) external (i.e., fixed) versus internal (i.e., sequential) sampling-based approximation of the expectation operator; (c) constraint penalization as relaxations of feasibility; and (d) convexification of nonconvexity and nondifferentiability via surrogation. The integration of these techniques for solving the affine chance-constrained stochastic program (ACC-SP) with various degrees of practicality and computational efforts is the main contribution of this paper.
