Multivariate Spectral Gradient Algorithm for Nonsmooth ConvexOptimization Problems

Abstract EN

We propose an extended multivariate spectral gradient algorithm to solvethe nonsmooth convex optimization problem.

First, by using Moreau-Yosida regularization, we convert the original objective function to a continuously differentiable function; then we use approximate function and gradient values of the Moreau-Yosida regularization to substitute the corresponding exact values in the algorithm.

The global convergence is proved under suitable assumptions.

Numerical experiments are presented to show the effectiveness of this algorithm.