Abstract
We consider finite dimensional optimization problems depending on one real parameter t. Recently, Jongen/Jonker/Twilt [9] studied the generic behaviour of such problems. Based on this investigation, we propose a partial concept for finding a suitably fine discretization 0=to<…<ti−1<ti<…<tN=1 of the interval [0,1], and corresponding local minima x(ti), i=1,…,N; here, information on the point x(ti-1) is used in order to compute x(ti). Mainly, socalled continuation methods can be exploited. However, at some parameter values, the branch of local minima used might have an endpoint; at such points one has to jump to another branch of local minima in order to continue the execution of the desired process. In case that the feasible set in a neighborhood of such a mentioned endpoint remains nonempty for increasing parameter values, it will be shown how a jump can be realized.
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© 1988 Springer-Verlag
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Guddat, J., Jongen, H.T., Nowack, D. (1988). Parametric optimization: Pathfollowing with jumps. In: Gómez-Fernandez, J.A., Guerra-Vázquez, F., López-Lagomasino, G., Jiménez-Pozo, M.A. (eds) Approximation and Optimization. Lecture Notes in Mathematics, vol 1354. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0089582
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DOI: https://doi.org/10.1007/BFb0089582
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