On characterizing the solution sets of pseudolinear programs Technical Note DOI:
Cite this article as: Jeyakumar, V. & Yang, X.Q. J Optim Theory Appl (1995) 87: 747. doi:10.1007/BF02192142 Abstract
This paper provides several new and simple characterizations of the solution sets of pseudolinear programs. By means of the basic properties of pseudolinearity, the solution set of a pseudolinear program is characterized, for instance, by the equality that
\(\nabla f(x)^T (\bar x - x) = 0\), for each feasible point x, where \(\bar x\) is in the solution set. As a consequence, we give characterizations of both the solution set and the boundedness of the solution set of a linear fractional program. Key Words Solution sets pseudolinear programs linear fractional programs
Communicated by M. Avriel
Chew, K. L.
Choo, E. V.
Pseudolinearity and Efficiency
, Mathematical Programming, Vol. 28, pp. 226–239, 1984.
First and Second-Order Characterization of Pseudolinear Functions
, European Journal of Operations Research, Vol. 67, pp. 278–286, 1993.
On Pseudolinear Functions
, European Journal of Operations Research, Vol. 50, pp. 353–360, 1991.
Cooper, W. W.
Programming with Linear Fractional Functionals
, Naval Research Logistics Quarterly, Vol. 19, pp. 181–186, 1962.
Craven, B. D.
, Sigma Series in Applied Mathematics, Heldermann Verlag, Berlin, Germany, 1988.
Mangasarian, O. L.
A Simple Characterization of Solution Sets of Convex Programs
, Operations Research Letters, Vol. 7, pp. 21–26, 1988.
Burke, J. V.
Ferris, M. C.
Characterization of Solution Sets of Convex Programs
, Operations Research Letters, Vol. 10, pp. 57–60, 1991.
Infinite-Dimensional Convex Programming with Applications to Constrained Approximation
, Journal of Optimization Theory and Applications, Vol. 75, pp. 469–586, 1992.
Yang, X. Q.
Convex Composite Multi-Objective Nonsmooth Programming
, Mathematical Programming, Vol. 59, pp. 325–343, 1993.
Kortanek, K. O.
Evans, J. P.
Pseudoconcave Programming and Lagrange Regularity
, Operations Research, Vol. 15, pp. 882–892, 1967.
Rockafellar, R. T.
, Princeton University Press, Princeton, New Jersey, 1970.
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