## Optimization Seminar

Thursday, May 3, 2018 · 10:30 AM - Noon

**Title:**

*Solution Uniqueness of Convex Piecewise Affine Functions Based Optimization with Applications to Constrained l*

_{1}

*Minimization*

**Speaker:**Ahmad Mousavi

**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**

Abstract:

Abstract:

*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.