Regularization methods for optimization problems with probabilistic constraints
Regularization methods for optimization problems with probabilistic constraints
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DOI：
10.1007/s10107-012-0539-6
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发表时间：
2013-04-01
影响因子：
2.7
通讯作者：
Martinez, Gabriela
中科院分区：
文献类型：
--
作者：
Dentcheva, Darinka;Martinez, Gabriela
研究了随机右端非线性不等式上的概率约束非线性随机优化问题。我们发展了两种数值方法与正则化的数值解。该方法是基于一阶最优性条件和逐步生成的p-有效点的可行集的连续内逼近。该算法产生一个最佳的解决方案，涉及阿尔法凹概率分布的问题。对于任意分布，该算法解决了凸船体问题，并提供了最优值和近最优解的上下界。两个切割平面方法的方法进行了比较。
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.