 Constraint Qualifications in Maximization ProblemsKenneth Arrow, Leonid Hurwicz and Hirofumi Uzawa A chapter in Traces and Emergence of Nonlinear Programming, 2014, pp 81-97 from Springer Abstract: Abstract Many problems arising in logistics and in the application of mathematics to industrial planning are in the form of constrained maximizations with nonlinear maxirnands 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. Keywords: Convex Cone; Constraint Qualification; Closed Convex Cone; Nondegeneracy Condition; Lagrangian Condition (search for similar items in EconPapers) There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it. Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-0348-0439-4_4 Ordering information: This item can be ordered from DOI: 10.1007/978-3-0348-0439-4_4 Access Statistics for this chapter More chapters in Springer Books from Springer |
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