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Quadratic Convex Reformulations for Integer and Mixed-Integer Quadratic Programs

In: Optimization and Control for Systems in the Big-Data Era

Author

Listed:
  • Baiyi Wu

    (Guangdong University of Foreign Studies)

  • Rujun Jiang

    (The Chinese University of Hong Kong)

Abstract

We review recent advances in the quadratic convex reformulation (QCR) approach that is employed to derive efficient equivalent reformulations for mixed-integer quadratically constrained quadratic programming (MIQCQP) problems. Although MIQCQP problems can be directly plugged into and solved by standard MIQP solvers that are based on branch-and-bound algorithms, it is not efficient because the continuous relaxation of the standard MIQCQP reformulation is very loose. The QCR approach is a systematic way to derive tight equivalent reformulations. We will explore the QCR technique on subclasses of MIQCQP problems with simpler structures first and then generalize it step by step such that it can be applied to general MIQCQP problems. We also cover the recent extension of QCR on semi-continuous quadratic programming problems.

Suggested Citation

  • Baiyi Wu & Rujun Jiang, 2017. "Quadratic Convex Reformulations for Integer and Mixed-Integer Quadratic Programs," International Series in Operations Research & Management Science, in: Tsan-Ming Choi & Jianjun Gao & James H. Lambert & Chi-Kong Ng & Jun Wang (ed.), Optimization and Control for Systems in the Big-Data Era, chapter 0, pages 43-58, Springer.
    • Handle: RePEc:spr:isochp:978-3-319-53518-0_4
    DOI: 10.1007/978-3-319-53518-0_4
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