Exploiting Structure in Nonsmooth Optimization Problems

优化，最小化或最大化函数的研究，是现代社会的基本。 应用非常多样化，包括以下问题：在设计新建道路时最小化建筑成本，最大化新微芯片设计的效率（速度），最小化预期的医院病床拥挤，以及最大化地震阻尼器在建筑物改造中的有效性。 尽管计算能力呈指数级增长，算法设计也有显著改进，但现代优化应用比以往任何时候都更加复杂。在这个提案中，我们推进了优化应用，算法设计和优化理论的研究和知识。

Optimization, the study of minimizing or maximizing a function, is essential in modern society. Applications are extremely diverse and include problems like: minimizing the construction costs when designing new roads, maximizing the efficiency (speed) of a new microchip design, minimizing expected hospital bed congestion, and maximizing the effectiveness of seismic dampers in building retrofitting. Despite the exponential growth in computing power and significant improvements in algorithm designs, modern applications of optimization are more complex than ever. In this proposal, we advance research and knowledge in Optimization Applications, Algorithm Design, and Optimization Theory.