Differential
Inclusions, Control and Optimization 20 (2000) 245-255

doi: 10.7151/dmdico.1014

Ewa M. Bednarczuk

*Systems Research Institute, PAS
01-447 Warsaw, Newelska 6, Poland*

In this paper we investigate the lower Lipschitz continuity of minimal points of an arbitrary set A depending upon a parameter u . Our results are formulated with the help of the modulus of minimality. The crucial requirement which allows us to derive sufficient conditions for lower Lipschitz continuity of minimal points is that the modulus of minimality is at least linear. The obtained results can be directly applied to stability analysis of vector optimization problems.

**Keywords:** minimal points, Lipschitz continuity, vector optimization.

**1991 Mathematics Subject Classification:** 90C29, 90C48.

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Received 5 January 2000

Revised 13 April 2000