Tractable Approximations of Chance Constrained Optimization Problems

这笔赠款提供资金，用于开发具有机会约束的优化问题的算法。在各种各样的应用中，不确定性是计划和决策的一个组成部分。这项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。将一种新的方法应用于机会约束优化问题，其中计算上难以处理的机会约束被有效地用可计算的凸约束来逼近，从而最终得到一个有效可解的逼近问题。当逼近是安全的时，这种方法特别吸引人，因为它的可行集包含在机会约束问题的可行集内，使得逼近的每一个可行解对原问题都是可行的。安全可处理近似使得以计算高效和可靠的方式处理机会约束成为可能；在许多应用中，特别是在大规模应用中，这些优点显著地超过了该方法的固有缺点--保守性。如果成功，该研究将导致对具有随机数据的凸问题的安全可处理近似的深入研究。它将加强决策数学模型的建立和处理，并将显著扩大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。这项研究还将为困难的组合优化问题带来改进的算法。这项研究的应用领域包括制造、运输物流和金融工程。总体而言，这项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.