Exploiting Structure in Nonsmooth Optimization Problems

优化，即研究函数的最小化或最大化，在现代社会中是必不可少的。应用非常多样化，包括这样的问题：在设计新道路时最大限度地降低建筑成本，最大限度地提高新的微芯片设计的效率（速度），最大限度地减少预期的医院床位拥堵，以及在建筑改造中最大限度地提高地震阻尼器的有效性。尽管计算能力呈指数级增长，算法设计也有了重大改进，但现代优化应用比以往任何时候都更加复杂。在本提案中，我们推进优化应用，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.