**
ACTA MATHEMATICA UNIVERSITATIS COMENIANAE **

Vol. 65, 2 (1996)

pp. 229-245

DUALITY OF TRANSFORMATION FUNCTIONS IN THE INTERIOR POINT METHODS

M. HALICKA and M. HAMALA

**Abstract**.
In this paper a duality of transformation functions in the interior point method is treated. A dual pair of convex or linear programming problems is considered and the primal problem is transformed by the parametrized transformation function of a more general form than logarithmic is. The construction of the parametrized transformation function for the dual problem is carried out so that both transformation functions were dual. The result obtained explains the unlucid construction of dual transformation functions so far known as a special case of a simple general principle of constructing dual transformation functions.

**AMS subject classification**.
90C25; Secondary 90C05, 90C30

**Keywords**.
Linear programming, convex programming, interior point methods, transformation function, dual problem

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