Publisher: Bachudo Science Co. Ltd

Some Optimality Conditions For The Existence of Optimizers of Certain Class of Linear Programming Problems

M. U. Umoren
KEYWORDS: Linear Programming, d-function, Linear Exchange Algorithm, Optimal Experimental Design.

ABSTRACT:

it is well known that the optimum of a Linear Programming problem occurs at an extremum point of the feasible region. This paper considers some other optimality conditions for the existence of optimizers of Linear Programming (LP) problems based on the principles of optimal experimental design. It is shown in this work, for example, that;  i} The optimizer of an LP Problem occurs at a point, which the d·function isminimum within the feasible region.ii} The d-function at the end point of the kth iteration is less than the d·function at any other point within the experimental space.(iii) The d·function at the minimizer x is the maximum of the minimum d-functions for k differont iterations. This is a first-order necessary condition for the existence ot a minimizer of an LP problem.


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