Incremental Subgradient Methods for Nondifferentiable Optimization

Incremental Subgradient Methods 1 for Nondifferentiable Optimization

We consider a class of subgradient methods for minimizing a convex function that consists of the sum of a large number of component functions. This type of minimization arises in a dual context from Lagrangian relaxation of the coupling constraints of large scale separable problems. The idea is to perform the subgradient iteration incrementally, by sequentially taking steps along the subgradien...

Nondifferentiable Optimization with Epsilon Subgradient Methods

To Appear in SIAM J . on Optimization INCREMENTAL SUBGRADIENT METHODS 1 FOR NONDIFFERENTIABLE OPTIMIZATION

We consider a class of subgradient methods for minimizing a convex function that consists of the sum of a large number of component functions. This type of minimization arises in a dual context from Lagrangian relaxation of the coupling constraints of large scale separable problems. The idea is to perform the subgradient iteration incrementally, by sequentially taking steps along the subgradien...

Nondifferentiable Optimization via Approximation*

Optimization problems with nondifferentiable cost functionals, particularly minimax problems, have received considerable attention recently since they arise naturally in a variety of contexts. Optimality conditions for such problems have been derived by several authors while a number of computational methods have been proposed for their solution (the reader is referred to [1] for:a fairly compl...

A Direct Splitting Method for Nonsmooth Variational Inequalities

We propose a direct splitting method for solving nonsmooth variational inequality problems in Hilbert spaces. The weak convergence is established, when the operator is the sum of two point-to-set and monotone operators. The proposed method is a natural extension of the incremental subgradient method for nondifferentiable optimization, which explores strongly the structure of the operator using ...