Optimization methods in operations management and economics

我和我的合作者一起开发优化模型和方法来解决运营管理、经济学和相关领域的问题。一个共同的主线是开发新的优化工具和应用于实际问题的理论观点。我们的工作有助于五个主要研究领域：(a)优化中的投影和对偶理论(b)整数规划博弈(c)新型优化理论在契约研究中的应用(d)新型优化理论在长期规划问题中的应用(e)最坏情况不确定性下的优化关于(a)，投影和对偶是用于理解优化问题结构的常用工具。我们研究了离散和连续优化中投影的一般原理，特别是经典傅里叶-莫兹金方法在新情况下的扩展。我们计划在未来几年探索投射和二元性之间更丰富的联系。关于(b)，涉及决策者离散决策的战略博弈（称为“整数规划博弈”）具有重要的应用，但与连续博弈相比，研究较少。我的工作是探索具有整数决策的游戏的可计算性和可表征性的理论问题。关于(c)，许多复杂的企业必须设计契约来协调众多决策者的努力。一般来说，契约设计是一个困难的优化问题。我们利用对偶性和最优性条件的新方法来研究合同设计中的理论问题。我们计划研究如何将来自新优化技术的新见解应用于实际承包环境，例如运营管理环境中的多任务处理。关于(d)，经济比以往任何时候都更加紧密地联系在一起。企业必须计划“永远在线”，并对不断变化的环境做出反应。这就产生了具有挑战性的无限视界优化问题，这些问题逃避了传统的分析形式。我们开发了新的优化技术，包括将标准算法扩展到无限维的相应算法。最后，对于(e)，我们研究了假设决策者面临最坏情况不确定性的优化问题。在一个每天都有新的危机（经济、环境和社会）的世界里，能够为最坏的情况做计划是有商业意义的。许多现有的方法已被证明是保守的。我们探索新的优化技术，限定“最坏情况”的含义，并提供新的见解。

I develop, along with my collaborators, optimization models and methods to solve problems in operations management, economics, and related areas. A common thread is the development of novel optimization tools and theoretical perspectives that apply to practical problems. Our work contributes to five main research areas: (a) Projection and duality theory in optimization (b) Integer programming games (c) Applications of novel optimization theory to the study of contracts (d) Application of novel optimization theory to long-run -horizon planning problems (e) Optimization under worst-case uncertainty Regarding (a), projection and duality are common tools used to understand the structure of optimization problems. We study general principles of projection in discrete and continuous optimization, particularly extensions of the classical Fourier-Motzkin methodology to new settings. We plan to explore richer connections between projection and duality in the years ahead. Regarding (b), strategic games that involve discrete decisions by decision-makers (termed "integer programming games'') have important applications but have been less studied than their continuous counterparts. My work explores theoretical questions of computability and representability for games with integer decisions. Regarding (c), many complex businesses must design contracts to coordinate the efforts of numerous decision-makers. In general, contract design is a difficult optimization problem. We leverage new approaches to duality and optimality conditions to study theoretical questions in contract design. We plan to investigate how novel insights coming from new optimization techniques can be used in practical contracting settings, such as multitasking in operations management settings. Regarding (d), the economy has become more connected and on-demand than ever. Businesses must plan to be "always-on'' and responding to changing conditions. This gives rise to challenging infinite-horizon optimization problems that evade traditional forms of analysis. We develop novel optimization techniques, including extensions of standard algorithms to their infinite-dimensional counterparts. Finally, regarding (e), we study optimization problems where we assume that the decision-maker is facing worst-case uncertainty. In a world that brings fresh crises day by day (economic, environmental, and social), being able to plan for worst-case scenarios makes business sense. Many existing methodologies have proven to be conservative. We explore novel optimization techniques that qualify what is meant by "worst-case'' and provide fresh insights.