Composite Self-Concordant Minimization
We propose a variable metric framework for minimizing the sum of a self-concordant function and a possibly non-smooth convex function, endowed with an easily computable proximal operator. We theoretically establish the convergence of our framework without relying on the usual Lipschitz gradient assumption on the smooth part. An important highlight of our work is a new set of analytic step-size selection and correction procedures based on the structure of the problem. We describe concrete algorithmic instances of our framework for several interesting applications and demonstrate them numerically on both synthetic and real data.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Composite convex minimization involving self-concordant-like cost functions
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 self-concordant-like pro…
Minimizing Quasi-Self-Concordant Functions by Gradient Regularization of Newton Method
We study the composite convex optimization problems with a Quasi-Self-Concordant smooth component. This problem class naturally interpolates between classic Self-Concordant functions and functions with Lipschitz continuo…
Randomized block proximal damped Newton method for composite self-concordant minimization
In this paper we consider the composite self-concordant (CSC) minimization problem, which minimizes the sum of a self-concordant function $f$ and a (possibly nonsmooth) proper closed convex function $g$. The CSC minimiza…
Generalized Self-Concordant Functions: A Recipe for Newton-Type Methods
We study the smooth structure of convex functions by generalizing a powerful concept so-called self-concordance introduced by Nesterov and Nemirovskii in the early 1990s to a broader class of convex functions, which we c…
Vocal Bursts Type PredictionA Newton Frank-Wolfe Method for Constrained Self-Concordant Minimization
We demonstrate how to scalably solve a class of constrained self-concordant minimization problems using linear minimization oracles (LMO) over the constraint set. We prove that the number of LMO calls of our method is ne…
Experimental Design