AN INTERIORPOINT BASED SUBGRADIENT METHOD FOR NONDIFFERENTIABLE CONVEX OPTIMIZATION

We propose in this paper an algorithm for solving linearly constrained nondierentiable convex programming problems This algorithm combines the ideas of the ane scaling method with the subgradient method It is a generalization of the dual and interior point method for min max problems proposed by Sturm and Zhang 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 Key words Nondierentiable convex programming ane scaling search direction subgradient method AMS subject classication M