2026-09-19T00:53:48Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/93752022-01-13T07:54:48Zcom_1721.1_7582com_1721.1_7581col_1721.1_131023
Dimitris Bertsimas.
Tziligakis, Constantine Nikolaos
Massachusetts Institute of Technology. Operations Research Center.
Massachusetts Institute of Technology. Operations Research Center
Sloan School of Management
2005-08-22T20:42:19Z
2005-08-22T20:42:19Z
1999
1999
http://hdl.handle.net/1721.1/9375
44815245
Thesis (S.M.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 1999.
Includes bibliographical references (leaves 107-111).
We develop various algorithms for solving mixed integer-quadratic problems. These problems exhibit exponential complexity resulting from the presence of integer variables. Traditional approaches that apply in pure integer programming are not very helpful, since the existence of continuous variables in our problems complicates their use. Vie develop relaxation and heuristic algorithms designed so as to provide tight lower and upper bounds to the optimal solution of the mixed combinatorial problem. In some cases the obtained range, in which the optimum lies, is small enough to be considered satisfactory by itself. This has been accomplished in problems with up to 150 variables. Exact algorithms have also been developed and guarantee the optimal solution upon termination. The idea of Branch and Bound enhanced with the use of lower and upper bounds obtained with the aforementioned methods is implemented for that purpose. Problems with up to 70 variables have been solved. Our ideas and algorithms are applied to the Problem of Index and Portfolio Replication with a limited number of assets. This problem arises in Finance, but, in its more general form, can find application in various areas ranging from Statistics to Optimal Control and Manufacturing.
by Constantine Nikolaos Tziligakis.
S.M.
111 leaves
9078939 bytes
9078699 bytes
application/pdf
application/pdf
eng
Massachusetts Institute of Technology
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http://dspace.mit.edu/handle/1721.1/7582
Operations Research Center.
Relaxation and exact algorithms for solving mixed integer-quadratic optimization problems
Thesis
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<Abstract>We develop various algorithms for solving mixed integer-quadratic problems. These problems exhibit exponential complexity resulting from the presence of integer variables. Traditional approaches that apply in pure integer programming are not very helpful, since the existence of continuous variables in our problems complicates their use. Vie develop relaxation and heuristic algorithms designed so as to provide tight lower and upper bounds to the optimal solution of the mixed combinatorial problem. In some cases the obtained range, in which the optimum lies, is small enough to be considered satisfactory by itself. This has been accomplished in problems with up to 150 variables. Exact algorithms have also been developed and guarantee the optimal solution upon termination. The idea of Branch and Bound enhanced with the use of lower and upper bounds obtained with the aforementioned methods is implemented for that purpose. Problems with up to 70 variables have been solved. Our ideas and algorithms are applied to the Problem of Index and Portfolio Replication with a limited number of assets. This problem arises in Finance, but, in its more general form, can find application in various areas ranging from Statistics to Optimal Control and Manufacturing.</Abstract>
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