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Inductive linearization for binary quadratic programs with linear constraints

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  • Sven Mallach

    (University of Bonn)

Abstract

A linearization technique for binary quadratic programs (BQPs) that comprise linear constraints is presented. The technique, called “inductive linearization”, extends concepts for BQPs with particular equation constraints, that have been referred to as “compact linearization” before, to the general case. Quadratic terms may occur in the objective function, in the set of constraints, or in both. For several relevant applications, the linear programming relaxations obtained from applying the technique are proven to be at least as strong as the one obtained with a well-known classical linearization. It is also shown how to obtain an inductive linearization automatically. This might be used, e.g., by general-purpose mixed-integer programming solvers.

Suggested Citation

  • Sven Mallach, 2021. "Inductive linearization for binary quadratic programs with linear constraints," 4OR, Springer, vol. 19(4), pages 549-570, December.
    • Handle: RePEc:spr:aqjoor:v:19:y:2021:i:4:d:10.1007_s10288-020-00460-z
    DOI: 10.1007/s10288-020-00460-z
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    References listed on IDEAS

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    1. Fred Glover & Eugene Woolsey, 1973. "Further Reduction of Zero-One Polynomial Programming Problems to Zero-One linear Programming Problems," Operations Research, INFORMS, vol. 21(1), pages 156-161, February.
    2. Oral, Muhittin & Kettani, Ossama, 1992. "Reformulating nonlinear combinatorial optimization problems for higher computational efficiency," European Journal of Operational Research, Elsevier, vol. 58(2), pages 236-249, April.
    3. G. Dantzig & R. Fulkerson & S. Johnson, 1954. "Solution of a Large-Scale Traveling-Salesman Problem," Operations Research, INFORMS, vol. 2(4), pages 393-410, November.
    4. Warren P. Adams & Hanif D. Sherali, 1986. "A Tight Linearization and an Algorithm for Zero-One Quadratic Programming Problems," Management Science, INFORMS, vol. 32(10), pages 1274-1290, October.
    5. Sven Mallach, 2018. "Compact linearization for binary quadratic problems subject to assignment constraints," 4OR, Springer, vol. 16(3), pages 295-309, September.
    6. C. Helmberg & F. Rendl & R. Weismantel, 2000. "A Semidefinite Programming Approach to the Quadratic Knapsack Problem," Journal of Combinatorial Optimization, Springer, vol. 4(2), pages 197-215, June.
    7. Billionnet, Alain & Calmels, Frederic, 1996. "Linear programming for the 0-1 quadratic knapsack problem," European Journal of Operational Research, Elsevier, vol. 92(2), pages 310-325, July.
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