We propose in this paper an algorithm for solving linearly constrained nondifferentiable convex programming problems. This algorithm combines the ideas of the affine scaling method with the subgradient method. It is a generalization of the dual and interior point method for min-max problems proposed by J.F. Sturm and S. Zhang (1995), A dual and interior point approach to solve convex min-max problems, in D.-Z. Du and P.M. Pardalos (eds.), Minimax and Applications, pp. 69-78, Kluwer Academic Publishers. In the new method, the search direction is obtained by projecting in a scaled space a subgradient of the objective function with a logarithmic barrier term. The stepsize choice is analogous to the stepsize choice in the usual subgradient method. Convergence of the method is established.
- Affine scaling search direction
- Nondifferentiable convex programming
- Subgradient method