?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%2F4105%2F&rft.title=Large-Scale+Convex+Optimization+via+Saddle+Point+Computation&rft.creator=Kallio%2C+M.J.&rft.creator=Rosa%2C+C.H.&rft.description=This+article+proposes+large-scale+convex+optimization+problems+to+be+solved+via+saddle+points+of+the+standard+Lagrangian.+A+recent+approach+for+saddle+point+computation+is+specialized%2C+by+way+of+a+specific+perturbation+technique+and+unique+scaling+method%2C+to+convex+optimization+problems+with+differentiable+objective+and+constraint+functions.+In+each+iteration+the+update+directions+for+primal+and+dual+variables+are+determined+by+gradients+of+the+Lagrangian.+These+gradients+are+evaluated+at+perturbed+points+which+are+generated+from+current+points+via+auxiliary+mappings.+The+resulting+algorithm+suits+massively+parallel+computing.+Sparsity+can+be+exploited+efficiently.+Employing+simulation+of+parallel+computations%2C+an+experimental+code+embedded+into+GAMS+is+tested+on+two+sets+of+nonlinear+problems.+The+first+set+arises+from+multi-stage+stochastic+optimization+of+the+US+energy+economy.+The+second+set+consists+of+multi-currency+bond+portfolio+problems.+In+such+stochastic+optimization+problems+the+serial+time+appears+approximatively+proportional+to+the+number+of+scenarios%2C+while+the+parallel+time+seems+independent+of+the+number+of+scenarios.+Thus%2C+we+observe+that+the+serial+time+of+our+approach+in+comparison+with+Minos+increases+slower+with+the+problem+size.+Consequently%2C+for+large+problems+with+reasonable+precision+requirements%2C+our+method+appears+faster+than+Minos+even+in+a+serial+computer.&rft.publisher=WP-94-107&rft.date=1994-10&rft.type=Monograph&rft.type=NonPeerReviewed&rft.format=text&rft.language=en&rft.identifier=https%3A%2F%2Fpure.iiasa.ac.at%2Fid%2Feprint%2F4105%2F1%2FWP-94-107.pdf&rft.identifier=++Kallio%2C+M.J.+%3Chttps%3A%2F%2Fpure.iiasa.ac.at%2Fview%2Fiiasa%2F2005.html%3E+%26+Rosa%2C+C.H.+%3Chttps%3A%2F%2Fpure.iiasa.ac.at%2Fview%2Fiiasa%2F1541.html%3E++(1994).++Large-Scale+Convex+Optimization+via+Saddle+Point+Computation.+++IIASA+Working+Paper.+IIASA%2C+Laxenburg%2C+Austria%3A+WP-94-107+++++