Properties of an interior embedding for solving nonlinear optimization problems

Abstract

The paper presents a sufficient condition for the success of path, following algorithms with jumps when applied to one-parametric optimization problems. An interior embedding that always fulfils the mentioned sufficient condition is given. Finally, the assumption of regularity in the sense of Jongen, Jonker and Twilt is analysed for the presented embedding, and its genericity is proved, provided that it is formulated on the original data of the optimization problem used for the construction of the introduced interior embedding.