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

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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.