CAREER: Extensions of Stochastic Programming: Models, Algorithms, and Applications

这个教师早期职业发展（CAREER）奖是研究新的模型，算法和随机程序的应用与替代风险规避目标，主观概率和决策相关的不确定性。 虽然随机规划现在已经发展成为一个可行的范例规划和决策下的不确定性，在这一领域取得了很大的进展，在一些简化的假设为代价。例如，传统的随机规划涉及优化期望的目标函数。 其他常见的假设包括静态潜在概率分布的精确知识。然而，这些忽略风险的假设在许多实际应用中可能是非常不可取的。 不幸的是，这些推广通常会导致非凸优化模型。因此，（凸）随机规划的传统分解算法是不适用的。本研究将探讨非凸优化算法中分解原理的整合，以攻击这些一般随机程序的大规模实例。开发的概念将被应用到规划问题，在重要的经济部门，如加工工业，工程设计和公用事业行业。该职业发展计划的教育部分旨在推广基于工程教育和实践中的规划和决策的随机规划。为了实现这一目标，用户友好的随机规划建模和求解工具，电子教程，和真实的世界的案例studies.The运筹学界认识到随机规划作为一个有价值的定量技术，在面对不确定性的决策支持将开发。然而，这一工具尚未在实际规划和决策中得到广泛使用。原因有二：传统的随机规划模型对于现实生活中的应用来说通常过于简单，并且在工程教育中缺乏对实际随机规划概念的了解。建议的研究计划将扩展随机规划范式超越了一些传统的不切实际的假设。这些推广将需要开发全新的随机规划模型和算法，并将其应用于相关的实际问题。在教育方面，将开发用户友好的随机规划求解器，电子教程和工业案例研究，以促进在本科和研究生工程教育中引入应用随机规划概念。

This Faculty Early Career Development (CAREER) award is to study new models, algorithms, and applications of stochastic programs with alternative risk-averse objectives, subjective probabilities, and decision-dependent uncertainties. Although stochastic programming has now evolved as a viable paradigm for planning and decision-making under uncertainty, much of the progress in this area has been made at the expense of some simplifying assumptions. For example, traditional stochastic programming is concerned with optimizing an expected objective function. Other common assumptions include precise knowledge of a static underlying probability distribution. However, these risk ignoring assumptions can be quite undesirable in many practical applications. Unfortunately, these generalizations typically lead to non-convex optimization models. Consequently, traditional decomposition algorithms for (convex) stochastic programs are inapplicable. The research will investigate the integration of decomposition principles within non-convex optimization algorithms in order to attack large-scale instances of these general stochastic programs. The developed concepts will be applied to planning problems in important economic sectors such as process industries, engineering design, and utility industries. The educational component of this career development plan is aimed at popularizing stochastic programming based planning and decision making in engineering education and practice. Towards this goal, user-friendly stochastic programming modeling and solver tools, electronic tutorials, and real world case studies will be developed.The operations research community recognizes Stochastic Programming as a valuable quantitative technique for decision support in the face of uncertainty. However, this tool has not achieved widespread use in practical planning and decision-making. Two reasons for this are: traditional stochastic programming models can often be overly simplistic for real-life applications and the lack of exposure to practical stochastic programming concepts in engineering education. The proposed research program will extend stochastic programming paradigm beyond some of the traditional impractical assumptions. These generalizations will require the development of entirely new stochastic programming models and algorithms, and their application to relevant practical problems. On the education side, user friendly stochastic programming solver, electronic tutorials, and industrial case-studies will be developed to facilitate the introduction of applied stochastic programming concepts in undergraduate and graduate engineering education.