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Constraint qualifications in maximization problems

Author

Listed:
  • Kenneth J. Arrow
  • Leonid Hurwicz
  • Hirofumi Uzawa

Abstract

Many problems arising in logistics and in the application of mathematics to industrial planning are in the form of constrained maximizations with nonlinear maximands or constraint functions or both. Thus a depot facing random demands for several items may wish to place orders for each in such a way as to maximize the expected number of demands which are fulfilled; the total of orders placed is limited by a budget constraint. In this case, the maximand is certainly nonlinear. The constraint would also be nonlinear if, for example, the marginal cost of storage of the goods were increasing. Practical methods for solving such problems in nonlinear programming almost invariably depends on some use of Lagrange multipliers, either by direct solution of the resulting system of equations or by a gradient method of successive approximations (see [5], Part II). This article discusses a part of the sufficient conditions for the validity of the multiplier method.

Suggested Citation

  • Kenneth J. Arrow & Leonid Hurwicz & Hirofumi Uzawa, 1961. "Constraint qualifications in maximization problems," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 8(2), pages 175-191, June.
    • Handle: RePEc:wly:navlog:v:8:y:1961:i:2:p:175-191
    DOI: 10.1002/nav.3800080206
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    Cited by:

    1. Paulo D. Waquil & THOMAS L. COX, 1995. "Spatial Equilibrium with Intermediate Products: Implementation and Validation in the Mercosur," Wisconsin-Madison Agricultural and Applied Economics Staff Papers 388, Wisconsin-Madison Agricultural and Applied Economics Department.
    2. Paulo D. WAQUIL & Thomas L. COX, 1995. "Spatial Equilibrium With Intermediate Products: Implementation And Validation In The Mercosur," Staff Papers 388, University of Wisconsin Madison, AAE.
    3. Francisco Lozano & Jonathan Moreno, 2018. "¿Se comparte la misma idea al utilizar el término Neoclasicismo?," Revista Cuadernos de Economia, Universidad Nacional de Colombia, FCE, CID, vol. 37(73), February.
    4. Geir B. Asheim & Tapan Mitra, 2021. "Characterizing sustainability in discrete time," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(2), pages 461-481, March.
    5. Jean‐Paul Chavas & Zohra Bouamra Mechemache, 2006. "The Economic Efficiency of Policy Reform and Partial Market Liberalization under Transaction Costs," Bulletin of Economic Research, Wiley Blackwell, vol. 58(3), pages 161-191, July.
    6. Shan Jiang & Shu-Cherng Fang & Qingwei Jin, 2021. "Sparse Solutions by a Quadratically Constrained ℓ q (0 < q < 1) Minimization Model," INFORMS Journal on Computing, INFORMS, vol. 33(2), pages 511-530, May.
    7. Erlanson, Albin & Kleiner, Andreas, 2020. "Costly verification in collective decisions," Theoretical Economics, Econometric Society, vol. 15(3), July.
    8. Suresh P. Sethi & Sushil Gupta & Vipin K. Agrawal & Vijay K. Agrawal, 2022. "Nobel laureates’ contributions to and impacts on operations management," Production and Operations Management, Production and Operations Management Society, vol. 31(12), pages 4283-4303, December.
    9. Robin Bade, 1973. "Optimal Foreign Investment and International Trade," The Economic Record, The Economic Society of Australia, vol. 49(1), pages 62-75, March.

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