Projections Onto Convex Sets (POCS) Based Optimization by Lifting
Abstract
Two new optimization techniques based on projections onto convex space (POCS) framework for solving convex and some non-convex optimization problems are presented. The dimension of the minimization problem is lifted by one and sets corresponding to the cost function are defined. If the cost function is a convex function in R^N the corresponding set is a convex set in R^(N+1). The iterative optimization approach starts with an arbitrary initial estimate in R^(N+1) and an orthogonal projection is performed onto one of the sets in a sequential manner at each step of the optimization problem. The method provides globally optimal solutions in total-variation, filtered variation, l1, and entropic cost functions. It is also experimentally observed that cost functions based on lp, p<1 can be handled by using the supporting hyperplane concept.
Cite
@article{arxiv.1306.2516,
title = {Projections Onto Convex Sets (POCS) Based Optimization by Lifting},
author = {A. Enis Cetin and Alican Bozkurt and Osman Gunay and Y. Hakan Habiboglu and Kivanc Kose and Ibrahim Onaran and R. A. Sevimli},
journal= {arXiv preprint arXiv:1306.2516},
year = {2013}
}