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Abstract: 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... (Update)
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.... 1] First, we ask for a sufficient condition with respect to the set M( 1 ) E(p) which we will call, as in other papers (cf. e.g. 4] 11] [2]) the Enlarged Mangasarian Fromovitz Constraint Qualification (briefly EnMFCQ) Let (F; G) 2 C 1 (IR n ; IR) s l . The EnMFCQ for...
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BibTeX entry: (Update)
Fandom Noubiap, R. (1997) : On Modifications of the Standard Embedding in Nonlinear Optimization, in : Guddat, J., Jongen, H.Th., Nozicka, F. Still, G., Twilt, F. (eds.): Parametric Optimization and Related Topics IV, Ser. Approximation and Optimization, Peter Lang Verlag http://citeseer.ist.psu.edu/noubiap97modifications.html More
@misc{ noubiap97modifications,
author = "F. Noubiap",
title = "On Modifications of the Standard Embedding in Nonlinear Optimization",
text = "Fandom Noubiap, R. (1997) : On Modifications of the Standard Embedding
in Nonlinear Optimization, in : Guddat, J., Jongen, H.Th., Nozicka, F. Still,
G., Twilt, F. (eds.): Parametric Optimization and Related Topics IV, Ser.
Approximation and Optimization, Peter Lang Verlag",
year = "1997",
url = "citeseer.ist.psu.edu/noubiap97modifications.html" }
Citations (may not include all citations):53 Differential Topology (context) - Hirsch - 1976
15 Singularity Theory and an Introduction to Catastrophe theory (context) - Lu - 1976
10 Critical sets in parametric optimization (context) - Jongen, Th et al. - 1986
10 Pathfollowing Methods in Nonlinear Optimization II: Exact Pe.. (context) - Dentcheva, Gollmer et al.
10 Pathfollowing Methods in Nonlinear Optimization III: Lagrang.. (context) - Dentcheva, Guddat et al. - 1995
10 Pathfollowing methods in Nonlinear Optimization I: Penalty E.. (context) - Gollmer, Guddat et al.
10 Parametric Optimization: Singularities (context) - Guddat, Guerra et al. - 1990
7 Introduction to numerical continuation methods (context) - Allgower, Georg - 1990
7 Finding zeros of maps: homotopy methods that are constructiv.. (context) - Chow, Mallet-Paret et al. - 1978
6 On stability and stationary points in nonlinear optimization (context) - Guddat, Jongen et al. - 1986
5 Nonlinear Optimization in IR n (context) - Jongen, Th et al. - 1983
5 Nonlinear Optimization in IR n (context) - Jongen, Th et al. - 1983
4 Pathfollowing methods for KuhnTucker curves by an active ind.. (context) - Gfrerer, Guddat et al. - 1985
4 Continuous deformation of nonlinear programs (context) - Kojima, Hirabayashi - 1984
3 Implementation of a pathfollowing procedure for solving nonl.. (context) - Wendler - 1993
2 On linear quadratic pertubations in one-parametric nonlinear.. (context) - Ruckmann, Tammer - 1992
2 An exact penalty function method with global convergence pro.. (context) - Di Pillo, Grippo - 1986
2 Kurvenverfolgung in der nichtlinearen Optimierung: uber die .. (context) - Noubiap - 1995
2 Parametric Optimization and Related Topics III (context) - Guddat, Jongen - 1993
1 A globally convergent algorithm based on embedding and param.. (context) - Gfrerer, Guddat et al. - 1983
1 Teubner Verlagsgesellschaft (context) - Gunther, Beyer et al. - 1973
1 Uber Verallgemeinerung konvexer Funktionen in linearen Raume.. (context) - Folgmann - 1974
1 Computerprogram PAFO (context) - Gollmer, Kausmann et al. - 1995
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