caa a22 4500 465775136 CHVBK 20180323111939.0 cr unu---uuuuu 170327e19901201xx s 000 0 eng 10.1007/BF02055201 doi (NATIONALLICENCE)springer-10.1007/BF02055201 Poore Aubrey Department of Mathematics, Colorado State University, 80523, Fort Collins, CO, USA aut Bifurcations in parametric nonlinear programming [Elektronische Daten] [Aubrey Poore] Bifurcation and continuation techniques are introduced as a class of methods for investigating the parametric nonlinear programming problem. Motivated by the Fritz John first-order necessary conditions, the parametric programming problem is first reformulated as a closed system of nonlinear equations which contains all Karush-Kuhn-Tucker and Fritz John points, both feasible and infeasible solutions, and relative minima, maxima, and saddle points. Since changes in the structure of the solution set and critical point type can occur only at singularities, necessary and sufficient conditions for the existence of a singularity are developed in terms of the loss of a complementarity condition, the linear dependence constraint qualification, and the singularity of the Hessian of the Lagrangian on a tangent space. After a brief introduction to elementary bifurcation theory, some simple singularities in this parametric problem are analyzed for both branching and persistence of local minima. Finally, a brief introduction to numerical continuation and bifurcation procedures is given to indicate how these facts can be used in a numerical investigation of the problem. J.C. Baltzer A.G. Scientific Publishing Company, 1990 Bifurcation nationallicence singularities nationallicence continuation nationallicence parametric nonlinear programming nationallicence stability nationallicence Annals of Operations Research Baltzer Science Publishers, Baarn/Kluwer Academic Publishers 27/1(1990-12-01), 343-369 0254-5330 27:1<343 1990 27 10479 https://doi.org/10.1007/BF02055201 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02055201 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Poore Aubrey Department of Mathematics, Colorado State University, 80523, Fort Collins, CO, USA aut NATIONALLICENCE 773 0- Annals of Operations Research Baltzer Science Publishers, Baarn/Kluwer Academic Publishers 27/1(1990-12-01), 343-369 0254-5330 27:1<343 1990 27 10479 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer