Self-concordant Tree and Decomposition Based Interior Point Methods for Stochastic Convex Optimization Problem

Michael Chen; Sanjay Mehrotra

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SPEPS Preprint

Author(s):	Michael Chen, Northwestern University, Evanston Sanjay Mehrotra, Northwestern University, Evanston
Title:	Self-concordant Tree and Decomposition Based Interior Point Methods for Stochastic Convex Optimization Problem
Date of Acceptance:	08.07.2007
Submission Date:	24.05.2007
Series Title:	Stochastic Programming E-Print Series (SPEPS)
Editors:	Julie L. Higle; Werner Römisch; Surrajeet Sen
Complete Preprint:	pdf (urn:nbn:de:kobv:11-10078826)
Submitted in:	Mathematical Programming (A)
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Abstract (eng):

We consider barrier problems associated with two and multistage stochastic convex optimization problems. We show that the barrier recourse functions at any stage form a self- concordant family with respect to the barrier parameter. We also show that the complexity value of the ﬁrst stage problem increases additively with the number of stages and scenarios. We use these results to propose a prototype primal interior point decomposition algorithm for the two-stage and multistage stochastic convex optimization problems admitting self-concordant barriers.

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