An interior point subgradient method for linearly constrained nondifferentiable convex programming

Hans Frenk, J.F. Sturm and Shuzhong Zhang

No EI 9612-/A, Econometric Institute Research Papers from Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute

Abstract: 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 Sturm and Zhang [J.F. Sturm and S. Zhang, A dual and interior point approach to solve convex min-max problems, in: D.-Z. Du and P.M. Pardalos eds., Minimax and Applications, (1995) 69-78, Kluwer]. 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.

Keywords: affine scaling; interior point method; nondifferentiable convex programming; subgradient (search for similar items in EconPapers)
Date: 1996-01-01
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Persistent link: https://EconPapers.repec.org/RePEc:ems:eureir:1376

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