Regularization methods for optimization problems with probabilistic constraints
成果类型：
Article
署名作者：
Dentcheva, Darinka; Martinez, Gabriela
署名单位：
Stevens Institute of Technology
刊物名称：
MATHEMATICAL PROGRAMMING
ISSN/ISSBN：
0025-5610
DOI：
10.1007/s10107-012-0539-6
发表日期：
2013
页码：
223-251
关键词：
摘要：
We analyze nonlinear stochastic optimization problems with probabilistic constraints on nonlinear inequalities with random right hand sides. We develop two numerical methods with regularization for their numerical solution. The methods are based on first order optimality conditions and successive inner approximations of the feasible set by progressive generation of p-efficient points. The algorithms yield an optimal solution for problems involving alpha-concave probability distributions. For arbitrary distributions, the algorithms solve the convex hull problem and provide upper and lower bounds for the optimal value and nearly optimal solutions. The methods are compared numerically to two cutting plane methods.
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