New approximation methods for solving binary quadratic programming problem

Yang, Rui

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https://hdl.handle.net/2142/16477 Copy

Description

Title

New approximation methods for solving binary quadratic programming problem

Author(s)

Yang, Rui

Issue Date

2010-06-22T19:37:18Z

Director of Research (if dissertation) or Advisor (if thesis)

Peng, Jiming

Department of Study

Industrial&Enterprise Sys Eng

Discipline

Systems & Entrepreneurial Engr

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

M.S.

Degree Level

Thesis

Date of Ingest

2010-06-22T19:37:18Z

Keyword(s)

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

Abstract

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.

Graduation Semester

2010-5

Permalink

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

Copyright and License Information

Copyright 2010 Rui Yang

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