Polyak's subgradient method with simplified projection for nondifferentiable optimization with linear constraints

Abstract

The projection operation required in the Polyak's subgradient method for nondifferentiable optimization problems with linear constraints is simplified. The modified method finds a new search direction in the cone of feasible directions at the current point. This greatly reduces the dimension of the projection operation. A computational test shows significant improvement in the computational efficiency.

AMS 1980 Subject Classifications:

• Primary: 90 C 30
• Secondary: 90 C 25

Keywords:

• Nondifferentiable optimization
• subgradient
• linearly constrained optimization