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  Home/Search   Document Details and Download   Summary   Related Articles

.... compact for all t 2 [0; 1) Finally, we discuss the assumption (A4) This is a condition to the parameter depending feasible set M 2 (t) for all t 2 [0; 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 M( 1 ) E(p) For all x 2 E(p) it holds: There exists a 2 IR n with (i) g j (x) Dg j (x) 0; j 2 fj 2 J j g j (x) 0g (ii) f k (x) Df k (x) 0; k 2 ....

....0g (ii) f k (x) Df k (x) 0; k 2 fk 2 K j f k (x) 0g (iii) 2x T 0 if kxk = p Theorem 3.13 Let (F; G) 2 C 1 (IR; IR) s l . Assume (A2) and the EnMFCQ. Then the MFCQ is satisfied for all x 2 M 2 (t) for all t 2 [0; 1] The proof runs along the lines of the proof of Theorem 10 in [2]. Remark 3.14 Using Theorem 2.8 we obtain that M 2 (0) is homeomorphic to M 2 (1) M( 1 ) E(p) and M 2 (0) is a convex set. This shows how restrictive the assumption EnMFCQ is. Second, we ask for a necessary and sufficient condition, where we follow the idea described for other embeddings in ....

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

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