Composite convex minimization involving self-concordant-like cost functions

Abstract. The self-concordant-like property of a smooth convex func- tion is a new analytical structure that generalizes the self-concordant notion. While a wide variety of important applications feature the self- concordant-like property, this concept has heretofore remained unex- ploited in convex optimization. To this end, we develop a variable metric framework of minimizing the sum of a \simple" convex function and a self-concordant-like function.We introduce a new analytic step-size selec- tion procedure and prove that the basic gradient algorithm has improved convergence guarantees as compared to \fast" algorithms that rely on the Lipschitz gradient property. Our numerical tests with real-data sets show that the practice indeed follows the theory.

Presented at:
Modelling, Computation and Optimization in Information Systems and Management Sciences (MCO 2015), Metz, France, May 11-13, 2015

 Record created 2016-07-26, last modified 2018-01-28

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