## Applied Mathematics Colloquium: Dr. Jianghai Hu

#### Purdue University

Friday, October 19, 2018 · 2 PM - 3 PM

**Title:**Distributed Solutions of Locally Coupled Convex Optimization Problems and Convex-Concave Games on Networks

**Speaker: **Jianghai Hu, Purdue University

**Abstract:**In this talk, we study the optimization problems for a group of agents whose individual objective functions and constraints depend on the variables of neighboring agents as modeled by a directed dependency graph. Several algorithms are proposed based on operator splitting techniques that can iteratively converge to an optimal primal (or dual) solution of the optimization problems. Then, via random coordinate updates, asynchronous implementations of the algorithms are developed with low computation and communication complexity and guaranteed almost sure convergence to an optimal solution. These algorithms are then extended for solving convex-concave games on agent networks played by two teams: each agent has local variables from both teams and a local payoff function dependent on the variables of its neighbors that is convex in the variables of one team and concave in the variables of the other, and the goal is to find a Nash equilibrium of the sum of all local payoff functions. Numerical results are presented to illustrate the proposed algorithms.