Optimization Seminar
Thursday, May 3, 2018 · 10:30 AM - 12 PM
Title: Solution Uniqueness of Convex Piecewise Affine Functions Based Optimization with Applications to Constrained l1 Minimization
Speaker: Ahmad Mousavi
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 l1 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 l1 minimization problems under possible polyhedral constraints.
An effective linear program based scheme is proposed to verify solution uniqueness conditions.
Speaker: Ahmad Mousavi
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 l1 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 l1 minimization problems under possible polyhedral constraints.
An effective linear program based scheme is proposed to verify solution uniqueness conditions.
