Algorithms for Large-Scale Cone and Convex Programs, Saddle-Point Problems and Variational Inequalities

这个项目的主要焦点是开发和/或复杂性分析的有效算法来解决凸优化(CO)问题。经济、自然科学和工程中的许多问题都可以归结为凸优化问题。特别是，为了解决极大的CO实例，这些方法包括CPU时间和内存空间要求较低的一阶方法。这项研究还将导致研究鞍点(SP)问题和变分不等式(VI)背景下的有效算法，因为它们与CO有着密切的联系。如果成功，这项研究的结果将导致：1)用于解决CO问题的新的和/或更好的算法；以及2)现有(例如，增广的拉格朗日惩罚)和/或新的(例如，块分解的变体)方法的新的复杂性结果。作为副产品，该项目还将导致开发新的软件包，这将增加和改进现有的工具，从业者可以用来解决在经济、自然科学和工程学的许多应用中出现的CO问题。

The main focus of this project is on the development and/or complexity analysis of efficient algorithms for solving convex optimization (CO) problems. Many problems in economics, natural sciences and engineering can be formulated as convex optimization (CO) problems. In particular, these include first-order methods with low CPU time and memory space requirements in order to solve extremely large CO instances. This investigation will also lead to the study efficient algorithms in the context of the saddle-point (SP) problem and variational inequalities (VI) due to their close connection to CO. New algorithms for solving CO will be developed by either handling the instance as is, or by reformulating it as a SP problem or VI, and then using an efficient algorithm for solving the reformulation.If successful, the results of this research will lead to: 1) new and/or better algorithms for solving CO problems, and; 2) new complexity results for existing (e.g., augmented Lagrangian penalty) and/or new (e.g., variants of the block-decomposition) methods. As a by-product, this project will also lead to the development of new software packages, which will increase and improve the existing tools available to practitioners for solving CO problems arising in many applications in economics, natural sciences, and engineering.