Relaxation and exact algorithms for solving mixed integer-quadratic optimization problems

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.

Department dc:contributor.department

Massachusetts Institute of Technology. Operations Research Center.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

1999

Author dc:creator

• Tziligakis, Constantine Nikolaos

Advisor dc:contributor.advisor

• Dimitris Bertsimas.

• Operations Research Center.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/9375

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/9375