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arXiv · 1306.2516

Projections Onto Convex Sets (POCS) Based Optimization by Lifting

A. Enis Cetin·Alican Bozkurt·Osman Gunay·Y. Hakan Habiboglu·Kivanc Kose·Ibrahim Onaran·R. A. Sevimli
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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.

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A. Enis Cetin, Alican Bozkurt, Osman Gunay, Y. Hakan Habiboglu, Kivanc Kose, Ibrahim Onaran, R. A. Sevimli. 2013-06-13. Projections Onto Convex Sets (POCS) Based Optimization by Lifting. https://arxiv.org/abs/1306.2516

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