Minimize for x ∈ RN the composite function F min x∈RN {F (x) = f(x) +ψ(x)} • f: RN → R, convex, differentiable, not strongly convex • ψ: RN → R ∪ {+∞}, convex, separable ψ(x) = n∑ i=1 ψi(x

elastic net). The algorithms use cyclical coordinate descent, computed along a regularization path. The methods can handle large problems and can also deal efficiently with sparse features. In comparative timings we find that the new algorithms are considerably faster than competing methods.

Coordinate descent algorithms solve optimization problems by successively performing approximate minimization along coordinate directions or coordinate hyperplanes. They have been used in applications for many years, and their popularity continues to grow because of their usefulness in data

Abstract. In this paper we present a novel randomized block coordinate descent method for the minimization of a convex composite objective function. The method uses (approximate) partial second-order (curvature) information, so that the algorithm performance is more robust when applied to highly

of the simplest of all, that uses a dichotomy procedure on each coordinate in turn. The resulting algorithm, termed Adaptive Coordinate Descent (ACiD), is analyzed on the Sphere function, and experimentally validated on BBOB testbench where it is shown to outperform the standard (1 +1)-CMA-ES, and is found

We study the convergence properties of a (block) coordinate descent method applied to minimize a nondifferentiable (nonconvex) function f(x1,...,xN) with certain separability and regularity properties. Assuming that f is continuous on a compact level set, the subsequence convergence

We propose a new stochastic coordinate descent method for minimizing the sum of convex functions each of which depends on a small number of coordinates only. Our method (APPROX) is simultaneously Accelerated, Parallel and PROXimal; this is the first time such a method is proposed. In the special

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In this paper we consider the problem of minimizing a convex function using a randomized block coordinate descent method. One of the key steps at each iteration of the algorithm is determining the update to a block of variables. Existing algorithms assume that in order to compute the update, a

Abstract not found