New approximation methods for solving binary quadratic programming problem

In this thesis, we consider a special class of binary quadratic programming problem (BQP) where the number of nonzero elements is fixed. Such problems arise frequently from various applications and have been proved to be NP-hard. After a brief review of the quadratic programming problem, several optimization algorithms are presented. In Chapter 3, we propose a new simple second order conic relaxation of the BQP problem. We derive some additional constraints based on the information from the data matrix. The algorithm will be compared with the existing SDP relaxation algorithm in terms of their numerical performances. In Chapter 4, we use the convex quadratic relaxation as a geometric embedding tool to reformulate the underlying BQP as a clustering problem, where the target is to find a single cluster of fixed size. This connection allows us to employ many effective clustering algorithm developed in the data mining field. A 2-approximation algorithm for the clustering problem is presented. Numerical results based on the new relaxation model and the proposed algorithm are reported. The last Chapter mainly discusses some theoretical results we put forward on the derived clustering problem. Core-set technique is used to derive a new algorithm, which can provide a (1+\epsilon) approximation ratio to the reformulated clustering problem.

Name thesis:degree_name

M.S.

Level thesis:degree_level

Thesis

Discipline thesis:degree_discipline

Systems & Entrepreneurial Engr

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2010

Author dc:creator

• Yang, Rui

Contributors dc:contributor

• Peng, Jiming

• Semidefinite Programming Relaxation
• Binary Quadratic Problem
• Approximation Algorithm
• Core-set Technique

Statement dc:rights

• Copyright 2010 Rui Yang

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/16477

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/16477