1999-05-24Buch DOI: 10.18452/2669
On double one-parametric optimization problems and some applications
This paper deals with a special class of quadratic optimization problems with quadratic constraints, which we call double parametric. We try to solve these problems using Pathfollowing Methods with a special case of the Standard Embedding. The singularity theory developed by Jongen, Jonker and Twilt plays a great role in our investigations. In cases where a jump from one connected component to another one in the set of local minimizers and in the set of generalized critical points is not possible, we prove that the turning points are in negative direction. We survey results with respect to the choice of the starting point and make some proposals in order to overcome cases where jumps are not possible. We show the role of the Mangasarian-Fromovitz constraints qualification in the existence of the jumps and the solution of considered problems. Some examples of applications to global quadratic optimization and multicriteria optimization are given.
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