A Sequential Algorithm for Solving Nonlinear
نویسندگان
چکیده
An algorithm is presented for solving nonlinear optimization problems with chance 5 constraints, i.e., those in which a constraint involving an uncertain parameter must be satisfied with at 6 least a minimum probability. In particular, the algorithm is designed to solve cardinality-constrained 7 nonlinear optimization problems that arise in sample average approximations of chance-constrained 8 problems, as well as in other applications in which it is only desired to enforce a minimum number 9 of constraints. The algorithm employs a novel penalty function, which is minimized sequentially 10 by solving quadratic optimization subproblems with linear cardinality constraints. Properties of 11 minimizers of the penalty function in relation to minimizers of the corresponding nonlinear opti12 mization problem are presented, and convergence of the proposed algorithm to a stationary point of 13 the penalty function is proved. The effectiveness of the algorithm is demonstrated through numerical 14 experiments with a nonlinear cash flow problem. 15
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