In optimization the term decomposition usually refers to iterative techniques for solving large problems that become block-separable after fixing certain coupling variables or removing coupling constraints.
By extension, the same techniques can be used to exploit other types of structure, for example, network or convolution structure. The most common decomposition approach is dual decomposition, often via the alternating direction method of multipliers (ADMM), or split Bregman method. In the dual approach coupling variables are handled by replicating the variables and enforcing equality through consistency constraints. In the talk we will discuss alternative decomposition schemes based on a direct splitting of the primal-dual optimality conditions. The techniques will be illustrated with examples from image deblurring.
Lieven Vandenberghe is Professor in the Electrical Engineering Department at UCLA, with a joint appointment in Mathematics. He received a Ph.D. in Electrical Engineering from K.U. Leuven, Belgium, in 1992. He joined UCLA in 1997, following postdoctoral appointments at K.U. Leuven and Stanford University, and has held visiting professor positions at K.U. Leuven and the Technical University of Denmark.
He is author (with Stephen Boyd) of the book Convex Optimization (2004) and editor (with Henry Wolkowicz and Romesh Saigal) of the Handbook of Semidefinite Programming (2000). His research interests are in optimization, systems and control, and signal processing.