A Sequential Algorithm for Solving Nonlinear Optimization Problems with Chance Constraints
提出一种序列算法，通过求解带线性基数约束的二次子问题来最小化精确惩罚函数，从而解决含机会约束的非线性优化问题，并在非线性现金流问题上验证了有效性。
An algorithm is presented for solving nonlinear optimization problems with chance constraints, i.e., those in which a constraint involving an uncertain parameter must be satisfied with at least a minimum probability. In particular, the algorithm is designed to solve cardinality-constrained nonlinear optimization problems that arise in sample average approximations of chance-constrained problems, as well as in other applications in which it is only desired to enforce a minimum number of constraints. The algorithm employs a novel exact penalty function which is minimized sequentially by solving quadratic optimization subproblems with linear cardinality constraints. Properties of minimizers of the penalty function in relation to minimizers of the corresponding nonlinear optimization problem are presented, and convergence of the proposed algorithm to stationarity with respect to the penalty function is proved. The effectiveness of the algorithm is demonstrated through numerical experiments with a nonlinear cash flow problem.