?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%2F4587%2F&rft.title=A+Penalty+Based+Simplex+Method+for+Linear+Programming&rft.creator=Swietanowski%2C+A.&rft.description=We+give+a+general+description+of+a+new+advanced+implementation+of+the+simplex+method+for+linear+programming.+The+method+%60%60decouples''+a+notion+of+the+simplex+basic+solution+into+two+independent+entities%3A+a+solution+and+a+basis.+This+generalization+makes+it+possible+to+incorporate+new+strategies+into+the+algorithm+since+the+iterates+no+longer+need+to+be+the+vertices+of+the+simplex.+An+advantage+of+such+approach+is+a+possibility+of+taking+steps+along+directions+that+are+not+simplex+edges+(in+principle+they+can+even+cross+the+interior+of+the+feasible+set).+It+is+exploited+in+our+new+approach+to+finding+the+initial+solution+in+which+global+infeasibility+is+handled+through+a+dynamically+adjusted+penalty+term.+%0D%0A%0D%0AWe+present+several+new+techniques+that+have+been+incorporated+into+the+method.+These+features+include%3A+previously+mentioned+method+for+finding+an+initial+solution%3B+an+original+approximate+steepest+edge+pricing+algorithm%3B+dynamic+adjustment+of+the+penalty+term.+%0D%0A%0D%0AThe+presence+of+the+new+crashing+and+restart+procedures+based+on+the+penalty+term+make+the+algorithm+particularly+suitable+for+sequential+%60%60warm+start''+calls+when+solving+subproblems+in+decomposition+approaches.+The+same+features+may+be+used+in+post+optimal+analysis.+%0D%0A%0D%0AThe+efficiency+of+the+new+features+is+demonstrated+when+running+the+method+on+a+subset+of+difficult+linear+programs+from+the+NETLIB+collection.&rft.publisher=WP-95-005&rft.date=1995-01&rft.type=Monograph&rft.type=NonPeerReviewed&rft.format=text&rft.language=en&rft.identifier=https%3A%2F%2Fpure.iiasa.ac.at%2Fid%2Feprint%2F4587%2F1%2FWP-95-005.pdf&rft.identifier=++Swietanowski%2C+A.+%3Chttps%3A%2F%2Fpure.iiasa.ac.at%2Fview%2Fiiasa%2F2438.html%3E++(1995).++A+Penalty+Based+Simplex+Method+for+Linear+Programming.+++IIASA+Working+Paper.+IIASA%2C+Laxenburg%2C+Austria%3A+WP-95-005+++++