On global quadratic growth condition for min-max optimization problems with quadratic functions

Abstract

Second-order sufficient condition and quadratic growth condition play important roles both in sensitivity and stability analysis and in numerical analysis for optimization problems. In this article, we concentrate on the global quadratic growth condition and study its relations with global second-order sufficient conditions for min-max optimization problems with quadratic functions. In general, the global second-order sufficient condition implies the global quadratic growth condition. In the case of two quadratic functions involved, we have the equivalence of the two conditions.

Keywords:

• mathematical programming
• global second-order sufficient condition
• quadratic growth condition
• min-max problems with quadratic functions

AMS Subject Classifications:

• 90C30; 90C46; 90C47

Notes

1 This work is partially supported by the Research Grants Council of Hong Kong (PolyU 529213).