2004-04-20Buch DOI: 10.18452/2950
Decomposition-based interior point methods for two-stage stochastic convex quadratic programs with recourse
Ozevin, M. Gokhan
Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, Institut für Mathematik
Zhao  recently showed that the log barrier associated with the recourse function of two-stage stochastic linear programs behaves as a strongly self-concordant barrier and forms a self concordant family on the first stage solutions. In this paper we show that the recourse function is also strongly self-concordant and forms a self concordant family for the two-stage stochastic convex quadratic programs with recourse. This allows us to develop Benders decomposition based linearly convergent interior point algorithms. An analysis of such an algorithm is given in this paper.  G. Zhao: A log-barrier method with Benders decomposition for solving two-stage stochastic linear programs, Mathematical Programming Ser. A 90, (2001) 507-536.
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