SOOCHOW JOURNAL OF MATHEMATICS

Volume 31, No. 2, pp. 273-289, April 2005




ON THE STABILITY OF LOCAL MINIMA

IN MATHEMATICAL PROGRAMMING

INVOLVING CONE-CONSTRAINTS


BY


DANG HOA AND DO VAN LUU



Abstract. In this paper, we establish conditions ensuring that the variation of the local minimum of a mathematical programming problem involving cone-constraints is of the same order of magnitude as the variation in the data. At the same time, we also show that the relative variation of Lagrange multipliers to the variation in the local minimum and in the data remains bounded.

-------------------------

Received December 5, 2003; revised March 18, 2004.

AMS Subject Classification. Primary 90C31; secondary 90C30.

Key words. cone-constraint, constraint qualification, stability, relative variation, perturbation analysis.

This research was partially supported by the Natural Science Council of Vietnam.