eprintid: 4587 rev_number: 22 eprint_status: archive userid: 351 dir: disk0/00/00/45/87 datestamp: 2016-01-15 02:06:30 lastmod: 2021-08-27 17:15:24 status_changed: 2016-01-15 02:06:30 type: monograph metadata_visibility: show item_issues_count: 2 creators_name: Swietanowski, A. creators_id: AL1272 title: A Penalty Based Simplex Method for Linear Programming ispublished: pub internal_subjects: iis_cmp internal_subjects: iis_met internal_subjects: iis_sys divisions: prog_opt abstract: We give a general description of a new advanced implementation of the simplex method for linear programming. The method ``decouples'' a notion of the simplex basic solution into two independent entities: 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. We present several new techniques that have been incorporated into the method. These features include: previously mentioned method for finding an initial solution; an original approximate steepest edge pricing algorithm; dynamic adjustment of the penalty term. The presence of the new crashing and restart procedures based on the penalty term make the algorithm particularly suitable for sequential ``warm start'' calls when solving subproblems in decomposition approaches. The same features may be used in post optimal analysis. The efficiency of the new features is demonstrated when running the method on a subset of difficult linear programs from the NETLIB collection. date: 1995-01 date_type: published publisher: WP-95-005 iiasapubid: WP-95-005 price: 10 creators_browse_id: 2438 full_text_status: public monograph_type: working_paper place_of_pub: IIASA, Laxenburg, Austria pages: 34 coversheets_dirty: FALSE fp7_type: info:eu-repo/semantics/book citation: Swietanowski, A. (1995). A Penalty Based Simplex Method for Linear Programming. IIASA Working Paper. IIASA, Laxenburg, Austria: WP-95-005 document_url: https://pure.iiasa.ac.at/id/eprint/4587/1/WP-95-005.pdf