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Defense Applications of Mathematical Programs with Optimization Problems in the Constraints

Author

Listed:
  • Jerome Bracken

    (Institute for Defense Analyses, Arlington, Virginia)

  • James T. McGill

    (Illinois Board of Higher Education, Springfield, Illinois)

Abstract

Bracken and McGill have discussed the theory, computations, and an example of mathematical programming models with optimization problems in the constraints [ Opns. Res. 21, 37–44 (1973)], and have presented a computer program for solving such models with nonlinear programs in the constraints [ Opns. Res. 22, 1097–1101 (1974)]. Bracken, Falk, and McGill have given a procedure for transforming mathematical programs with two-sided optimization problems in the constraints into mathematical programs with nonlinear programs in the constraints [ Opns. Res. 22, 1102–1104 (1974)], thus enabling their solution by the computer program. This paper formulates models of defense problems that are convex programs having the mathematical properties treated in the previous papers. The models include several strategic-force-planning models and two general-purpose-force planning models.

Suggested Citation

  • Jerome Bracken & James T. McGill, 1974. "Defense Applications of Mathematical Programs with Optimization Problems in the Constraints," Operations Research, INFORMS, vol. 22(5), pages 1086-1096, October.
    • Handle: RePEc:inm:oropre:v:22:y:1974:i:5:p:1086-1096
    DOI: 10.1287/opre.22.5.1086
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    Cited by:

    1. Johannes O. Royset & R. Kevin Wood, 2007. "Solving the Bi-Objective Maximum-Flow Network-Interdiction Problem," INFORMS Journal on Computing, INFORMS, vol. 19(2), pages 175-184, May.
    2. Ankur Sinha & Zhichao Lu & Kalyanmoy Deb & Pekka Malo, 2020. "Bilevel optimization based on iterative approximation of multiple mappings," Journal of Heuristics, Springer, vol. 26(2), pages 151-185, April.
    3. Gerald G. Brown & Antonios L. Vassiliou, 1993. "Optimizing disaster relief: Real‐time operational and tactical decision support," Naval Research Logistics (NRL), John Wiley & Sons, vol. 40(1), pages 1-23, February.
    4. Yunjia Ma & Wei Xu & Lianjie Qin & Xiujuan Zhao, 2019. "Site Selection Models in Natural Disaster Shelters: A Review," Sustainability, MDPI, vol. 11(2), pages 1-24, January.
    5. Benoît Colson & Patrice Marcotte & Gilles Savard, 2007. "An overview of bilevel optimization," Annals of Operations Research, Springer, vol. 153(1), pages 235-256, September.
    6. George E. Monahan, 1996. "Finding saddle points on polyhedra: Solving certain continuous minimax problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 43(6), pages 821-837, September.
    7. Allan Peñafiel Mera & Chandra Balijepalli, 2020. "Towards improving resilience of cities: an optimisation approach to minimising vulnerability to disruption due to natural disasters under budgetary constraints," Transportation, Springer, vol. 47(4), pages 1809-1842, August.
    8. Polyxeni-Margarita Kleniati & Claire Adjiman, 2014. "Branch-and-Sandwich: a deterministic global optimization algorithm for optimistic bilevel programming problems. Part I: Theoretical development," Journal of Global Optimization, Springer, vol. 60(3), pages 425-458, November.
    9. Joaquim Dias Garcia & Guilherme Bodin & Alexandre Street, 2024. "BilevelJuMP.jl: Modeling and Solving Bilevel Optimization Problems in Julia," INFORMS Journal on Computing, INFORMS, vol. 36(2), pages 327-335, March.
    10. Gabriel Lopez Zenarosa & Oleg A. Prokopyev & Eduardo L. Pasiliao, 2021. "On exact solution approaches for bilevel quadratic 0–1 knapsack problem," Annals of Operations Research, Springer, vol. 298(1), pages 555-572, March.

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