ACTA MATHEMATICA UNIVERSITATIS COMENIANAE
Vol. 61, 1 (1992)
pp. 41-55
MONOTONICITY OF THE LAGRANGIAN FUNCTION IN THE PARAMETRIC INTERIOR POINT METHODS OF CONVEX PROGRAMMING
M. HAMALA and M. HALICKA
Abstract.
Monotonicity of the Lagrangian function corresponding to the general root quasibarrier as well as to the general inverse barrier function of convex programming is proved. It is shown that monotonicity generally need not take place. On the other hand for LP-problems with some special structure monotonicity is proved for a very general class of interior point transformation functions.
AMS subject classification.
90C25; Secondary 90C05, 90C30
Keywords.
Convex programming, Lagrangian function, barrier function, quasibarrier function, interior point methods, dual problem
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