Tractable Approximations of Chance Constrained Optimization Problems

该补助金提供资金用于开发机会约束优化问题的算法。 不确定性是各种应用中规划和决策的组成部分。该研究将研究涉及罕见但代价高昂的事件的可能性的决策模型。 一种新的方法将被应用到机会约束优化问题，其中计算上难以处理的机会约束近似有效可计算的凸约束，从而结束了一个有效可解的近似问题。 该方法是特别有吸引力的近似是安全的，在这个意义上，它的可行集包含在机会约束问题的可行集，使每个可行的解决方案的近似是可行的原始问题。安全易处理的近似使得有可能处理机会约束的计算效率和可靠的方式，在许多应用中，特别是大规模的，这些优点显着超过固有的缺点的方法-它的conservatis.If成功的，研究将导致在深入调查的安全易处理的近似凸问题的随机数据。 它将加强决策数学模型的建立和处理，并将大大扩展支持现实生活决策的计算工具的范围和性能，从而提高其质量。 这项研究还将导致困难的组合优化问题的改进算法。 该研究的应用出现在制造业，运输物流和金融工程等领域。 在一般情况下，研究将有助于随机优化问题的计算工具和方法。

This grant provides funding to develop algorithms for optimization problems with chance constraints. Uncertainty is an integral part of planning and decision making in a wide variety of applications. The research will study decision models that involve the possibility of a rare but costly event. A novel approach will be applied to chance constrained optimization problems, where computationally intractable chance constraints are approximated by efficiently computable convex constraints, thus ending up with an efficiently solvable approximating problems. The approach is especially attractive when the approximation is safe, in the sense that its feasible set is contained in the feasible set of the chance constrained problem, so that every feasible solution of the approximation is feasible for the original problem. Safe tractable approximations make it possible to treat chance constraints in a computationally efficient and reliable fashion; in numerous applications, especially large scale ones, these advantages significantly outweigh the intrinsic shortcoming of the approach -- its conservatism.If successful, the research will result in an in-depth investigation of safe tractable approximations of convex problems with stochastic data. It will enhance the building and processing of mathematical models of decision making, and will extend significantly the scope and the performance of computational tools supporting real-life decision making, thus improving its quality. The research will also result in improved algorithms for difficult combinatorial optimization problems. Applications of the research arise in areas such as manufacturing, transportation logistics, and financial engineering. In general, the research will contribute to the computational tools and methodologies available for stochastic optimization problems.