2005-10-21Buch DOI: 10.18452/2537
On Modifications of the Standard Embedding in Nonlinear Optimization
This paper deals with pathfollowing methods in nonlinear optimization. We study the so- called "standard embedding" and show its limits. Then, we modify this embedding from several points of view and obtain modified standard embeddings having some advantages. Singularity theory developed by Jongen-Jonker-Twilt plays a great role in our investigation. In some cases, we have to jump from one connected component to another one in the set of local minimizers and in the set of generalized critical points, respectively. In the worst case, we have to find all connected components and that is still an open problem. Computationary results are presented.
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