Composite Convex Minimization Involving Self-concordant-Like Cost Functions.
Journal
Advances in Intelligent Systems and Computing
Journal Volume
359
Pages
155-168
Date Issued
2015
Author(s)
Abstract
The self-concordant-like property of a smooth convex function is a new analytical structure that generalizes the self-concordant notion. While a wide variety of important applications feature the selfconcordant- like property, this concept has heretofore remained unexploited 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 selection 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. © Springer International Publishing Switzerland 2015.
Other Subjects
Computation theory; Convex optimization; Cost functions; Functions; Information systems; Ion beams; Management science; Analytical structure; Convex functions; Convex minimization; Gradient algorithm; Improved convergence; Lipschitz gradients; Step size selection; Variable metric; Information management
Description
Metz, France
Type
conference paper