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Inexact Majorization-Minimization Method for Solving Structured Nonconvex Optimization Problems

By Dror Pan
Location Bloomfield 527
Advisor(s): Prof. Amir Beck Prof. Shoham Sabach
PhD
Academic Program: OR
 
Sunday 25 March 2018, 14:30 - 15:30

We suggest a majorization-minimization method for solving nonconvex minimization problems. The method is based on minimizing at each iterate a properly constructed consistent majorizer of the objective function. We describe a variety of classes of functions for which such a construction is possible. We intorduce an inexact variant of the method, in which only approximate minimization of the consistent majorizer is performed at each iteration. Both the exact and the inexact algorithms are shown to be descent methods whose accumulation points have a property which is stronger than standard stationarity. We give examples of cases in which the exact method can be applied. Finally, we show that the inexact method can be applied to a specific problem, called sparse source localization, by utilizing a fast optimization method on a smooth convex dual of its subproblems.

This talk is based on the work done as a part of the PhD research under the supervision of Prof. Amir Beck.