Polynomially solvable cases of binary quadratic programs

Duan Li, Xiaoling Sun, Shenshen Gu, Jianjun Gao, Chun Li Liu

Research output: Chapters, Conference Papers, Creative and Literary WorksRGC 12 - Chapter in an edited book (Author)peer-review

14 Citations (Scopus)

Abstract

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.
Original languageEnglish
Title of host publicationOptimization and Optimal Control
Subtitle of host publicationTheory and Applications
EditorsALTANNAR CHINCHULUUN, PANOS M. PARDALOS, RENTSEN ENKHBAT, IDER TSEVEENDORJ
PublisherSpringer Science+Business Media
Pages199-225
ISBN (Electronic)9780387894966
ISBN (Print)9780387894959
DOIs
Publication statusPublished - 2010
Externally publishedYes

Publication series

NameSpringer Optimization and Its Applications
Volume39
ISSN (Print)1931-6828
ISSN (Electronic)1931-6836

Research Keywords

  • Binary quadratic programming
  • Lagrangian dual
  • Logic circuit
  • Polynomial solvability
  • SDP relaxation
  • Seriesparallel graph

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