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办法已不再适用。气候、政治和经济变化引起的不确定性表明需要强有力的解决办法，而资源管理问题由于多个用户争夺稀缺资源而带有竞争色彩。实际上，兴趣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；一组用户都不想偏离的决策。简而言之，本研究的重点是解决竞争、不确定性和动态关系问题的理论和算法。这项工作将在大型网络市场的设计、控制、操作和模拟中得到应用。这项工作解决了在不确定性和动态复杂的情况下解决博弈论问题的理论和方法问题。更具体地说，我们关注随机动态均衡问题，特别是随机纳什和斯塔克尔伯格均衡问题及其动态扩展。真正的大规模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那些来自代表性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在一个专门的网站上及时发布获得的所有结果（理论，算法和软件），以便研究成果可以被其他研究人员，从业者和行业所利用，从而可以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.