Addressing Competition, Dynamics and Uncertainty in Optimization Problems: Theory, Algorithms, Applications and Grid-Computing Extensions

竞争的开始，加上社会及其支持经济日益网络化的性质，意味着现有的静态规划方法不再适当。气候、政治和经济变化带来的不确定性表明，需要强有力的解决方案，而资源管理问题已经呈现出一种竞争的色彩，多个用户争夺稀缺的资源。实际上，利益的问题已经从寻找最佳解决方案转变为确定用户策略的平衡；这是一组用户都不想偏离的决策。简而言之，这项研究侧重于解决存在于竞争、不确定性和动态之间的问题的理论和算法。这项工作将在大型网络化市场的设计、控制、运营和仿真中得到应用。这项工作解决了在充满不确定性和动力学的复杂环境中解决博弈论问题的理论和方法问题。更具体地说，我们主要研究随机动态均衡问题，特别是随机Nash和Stackelberg均衡问题及其动态推广。真正大规模的实例将通过异步网格计算扩展来解决。这项研究的一个重要组成部分在于本科生和来自代表不足群体的学生的参与。这项研究计划的另一个重要组成部分是将所有获得的结果(理论、算法和软件)及时发布在一个专门的网站上，以便研究成果可以与其他研究人员、实践者和行业合作，从而在全球范围内对教育和工业部门产生更广泛的影响。

The onset of competition coupled with the increasingly networked nature of societies and their supporting economies implies that the extant static planning approaches are no longer adequate. Uncertainties, arising from climactic, political and economic changes, suggest the need for robust solutions while resource management questions have taken on a competitive overtone with multiple users vying for scarce resources. In effect, the question of interest has shifted from that of finding the best solution to one of determining an equilibrium in user strategies; a set of decisions from which no user has a desire to deviate. In a nutshell, this study focuses on the theory and algorithms for addressing problems lying at the nexus of competition, uncertainty and dynamics. The work will find application in the design, control, operation and simulation of large networked markets. This work addresses theoretical and methodological questions underlying the solution of game-theoretic problems in settings complicated by uncertainty and dynamics. More specifically, we focus on stochastic dynamic equilibrium problems, particularly stochastic Nash and Stackelberg equilibrium problems as well as their dynamical extensions. Truly large-scale instances will be addressed by asynchronous grid-computing extensions. A strong component of this research lies in the involvement of both undergraduate students as well as those from under-represented groups. Another important component of this research program will be the timely posting of all the results (theory, algorithms and software) obtained on a dedicated website, so that the research output can be parlayed to other researchers, practitioners, and industry, and thus can have a much broader impact in educational and industrial sectors on a global scale.