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Mathematical Programming Models and Exact Algorithms

In: The Quadratic Unconstrained Binary Optimization Problem

Author

Listed:
  • Abraham P. Punnen

    (Simon Fraser University)

  • Renata Sotirov

    (Tilburg School of Economics and Management, Tilburg University)

Abstract

This chapter focusses on exact solution approaches for QUBO. We first discuss various mixed integer linear programming formulations, compare their relative strength in terms of LP relaxations, and resulting upper bounding strategies. Then, new developments based on semidefinite programming approaches are discussed in detail. The mathematical programming formulations discussed here can be used to solve small size problems and the resulting tight upper bounds on the optimal objective function values can be used in developing specialized enumerative algorithms. Capabilities of some promising enumerative algorithms and solvers are also briefly reviewed.

Suggested Citation

  • Abraham P. Punnen & Renata Sotirov, 2022. "Mathematical Programming Models and Exact Algorithms," Springer Books, in: Abraham P. Punnen (ed.), The Quadratic Unconstrained Binary Optimization Problem, chapter 0, pages 139-185, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-04520-2_6
    DOI: 10.1007/978-3-031-04520-2_6
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