Graduate Student Seminar

Speaker 1: Eswar Kammara

Title

Distributed Algorithm for solving a Linear Algebraic Equation

Abstract

In this seminar, we discuss a distributed algorithm for solving a linear algebraic equation of the form Ax = b, where A in n x n non singular matrix and b is an n-vector.

The equation is solved by a network of n agents assuming that each agent knows exactly one distinct row of the partitioned matrix [A b].  Each agent recursively updates its estimates of A^(-1)*b by utilizing current estimates generated by each of its neighbors.  Finally, we illustrate this algorithm with an example.

Speaker 2: Ahmad Mousavi

Title

Solution Uniqueness of Convex Piecewise Affine Functions Based Optimization with Applications to Constrained $\ell_1$ Minimization.

Abstract

In this talk, we study the solution uniqueness of an individual feasible vector of a class of convex optimization problems involving convex piecewise affine functions and subject to general polyhedral constraints.  This class of problems incorporates many important polyhedral constrained l_1 recovery problems arising from sparse optimization, such as basis pursuit, and LASSO. By leveraging the max-formulation of convex piecewise affine functions and convex analysis tools, we develop dual variables based necessary and sufficient uniqueness conditions via simple and yet unifying approaches; these conditions are applied to a wide range of l_1 minimization problems under possible polyhedral constraints. An effective linear program based scheme is proposed to verify solution uniqueness conditions.