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Necessary Conditions for Optimality for Paths Lying on a Corner

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  • Jason L. Speyer

    (The Charles Stark Draper Laboratory, Massachusetts Institute of Technology)

Abstract

A class of optimization problems is investigated in which some of the functions, continuous in all their arguments, have continuous right- and left-hand derivatives but are not equal at a point called the corner. For this nonclassical problem, a set of first order necessary conditions for stationarity is determined for an optimal path which may have arcs lying on a corner for a nonzero length of time. Enough conditions are provided to construct an extremal path. This, in part, is achieved by noting that the corner defines a manifold in which the derivatives of all the functions are uniquely defined. Three examples, two of which represent possible aggregate production and employment planning models, illustrate the theory.

Suggested Citation

  • Jason L. Speyer, 1973. "Necessary Conditions for Optimality for Paths Lying on a Corner," Management Science, INFORMS, vol. 19(11), pages 1257-1270, July.
    • Handle: RePEc:inm:ormnsc:v:19:y:1973:i:11:p:1257-1270
    DOI: 10.1287/mnsc.19.11.1257
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