Technical Note

Journal of Optimization Theory and Applications

, Volume 87, Issue 3, pp 747-755

First online:

On characterizing the solution sets of pseudolinear programs

  • V. JeyakumarAffiliated withDepartment of Applied Mathematics, University of New South Wales
  • , X. Q. YangAffiliated withDepartment of Mathematics, University of Western Australia

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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 pointx, 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