?url_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.relation=https%3A%2F%2Fpure.iiasa.ac.at%2Fid%2Feprint%2F4085%2F&rft.title=Preconditioned+Conjugate+Gradients+in+an+Interior+Point+Method+for+Two-stage+Stochastic+Programming&rft.creator=Gondzio%2C+J.&rft.description=We+develop+a+variant+of+an+interior+point+method+for+solving+two-stage+stochastic+linear+programming+problems.+The+problems+are+solved+in+a+deterministic+equivalent+form+in+which+the+first+stage+variables+appear+as+dense+columns.+To+avoid+their+degrading+influence+on+the+adjacency+structure+AA%5ET+(and+the+Cholesky+factor)+an+iterative+method+is+applied+to+compute+orthogonal+projections.+Conjugate+gradient+algorithm+with+a+structure-exploiting+preconditioner+is+used.+%0D%0A%0D%0AThe+method+has+been+applied+to+solve+real-life+stochastic+optimization+problems.+Preliminary+computational+results+show+the+feasibility+of+the+approach+for+problems+with+up+to+80+independent+scenarios+(a+deterministic+equivalent+linear+program+has+14001+constraints+and+63690+variables).&rft.publisher=WP-94-130&rft.date=1994-12&rft.type=Monograph&rft.type=NonPeerReviewed&rft.format=text&rft.language=en&rft.identifier=https%3A%2F%2Fpure.iiasa.ac.at%2Fid%2Feprint%2F4085%2F1%2FWP-94-130.pdf&rft.identifier=++Gondzio%2C+J.++(1994).++Preconditioned+Conjugate+Gradients+in+an+Interior+Point+Method+for+Two-stage+Stochastic+Programming.+++IIASA+Working+Paper.+IIASA%2C+Laxenburg%2C+Austria%3A+WP-94-130+++++