Paulo Mbunga
On double one-parametric optimization problems and some applications
Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976)

MSC:

90C30 Nonlinear programming

49M40 Methods of quadratic programming type, See also {90C20}

Abstract: 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.
Keywords: parametric optimization, pathfollowing methods, jumps, generalized critical point, turning point in the negative sense