Incremental Subgradient Methods for Nondifferentiable Optimization

Incremental Subgradient Methods 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...

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...

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 with Epsilon Subgradient Methods

An improved subgradient method for constrained nondifferentiable optimization

Polyak's subgradient method for constrained nondifferentiable optimization problems is modified in one respect to improve the computational efficiency. The two consecutive projection operations in Polyak method are combined into a single projection operation. The resulting algorithm has a convergence property which is strictly stronger than that of the original Polyak method. A computational te...