Polynomially Solvable Cases of Binary Quadratic Programs

Duan Li (), Xiaoling Sun (), Shenshen Gu (), Jianjun Gao () and Chunli Liu ()
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Duan Li: The Chinese University of Hong Kong
Xiaoling Sun: Fudan University
Shenshen Gu: Shanghai University
Jianjun Gao: The Chinese University of Hong Kong
Chunli Liu: Shanghai University of Finance and Economics

A chapter in Optimization and Optimal Control, 2010, pp 199-225 from Springer

Abstract: Summary We summarize in this chapter polynomially solvable subclasses of binary quadratic programming problems studied in the literature and report some new polynomially solvable subclasses revealed in our recent research. It is well known that the binary quadratic programming program is NP-hard in general. Identifying polynomially solvable subclasses of binary quadratic programming problems not only offers theoretical insight into the complicated nature of the problem but also provides platforms to design relaxation schemes for exact solution methods. We discuss and analyze in this chapter six polynomially solvable subclasses of binary quadratic programs, including problems with special structures in the matrix Q of the quadratic objective function, problems defined by a special graph or a logic circuit, and problems characterized by zero duality gap of the SDP relaxation. Examples and geometric illustrations are presented to provide algorithmic and intuitive insights into the problems.

Keywords: binary quadratic programming; polynomial solvability; series-parallel graph; logic circuit; lagrangian dual; SDP relaxation (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/978-0-387-89496-6_11

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