Primal-Dual Column Generation Method and Column Generation Decomposition with Degeneracy

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Soodbakhsh, Navid | 2014

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 46050 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Mahdavi Amiri, Nezameddin
Abstract:
Column generation technique has became a very important tool in the solution of linear programming problems. Column generation techniques start with solving a reduced version of the master problem. Recently, variations of the standard column generation approach have been proposed which use interior point of the dual feasible set instead of optimal slutions. So, primal-dual column generation technique uses a primal-dual interior point method to obtain well-centered non-optimal solutions of the restricted master problem. We show that the method converges to an optimal solution of the master problem. Then, an improved primal simplex algorithm (IPS) for degenerate linear problems is proposed. Indeed, this method is equivalent to a column generation decomposition. In this method, the problem is decomposed into two problems: reduced problem which is not degenerate or slightly degenerate and complementary problem. Finally, we implement these methods and comparatively test the programs on a variety of test problems
Keywords:
Interior Point Method ; Linear Programming ; Degenercy ; Column Generation Algorithm ; Primal Simplex Algorithm