Di Pillo, G. and Grippo, L., An exact penalty function method with global convergence properties for nonlinear programming problems, Math. Program. 36(1986), 1-18 44 R. Fandom Noubiap Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
On Modifications of the Standard Embedding in Nonlinear.. - Noubiap (1997) (1 citation) (Correct)
....Constraint Qualification (shortly EnMFCQ) is satisfied for the problem (P) if for all q q and for all x 2 B q (0) there exists a vector j 2 IR n such that: g j (x) Dg j (x)j 0; j 2 J; with g j (x) 0; 2x T j 0; if kxk 2 = q: Remark 4. 6 In the literature (cf. e.g. 10] 13] [5]) the EnMFCQ is known as a condition for the convergence of the penalty and exact penalty methods. Theorem 4.7 Assume that EnMFCQ is satisfied for the problem (P) Then the MFCQ is fulfilled for all x 2 M (t) and for all t 2 (0; 1] Furthermore if the set J 0 (x 0 ) fj 2 J jg j (x 0 ) ....
Di Pillo, G. and Grippo, L., An exact penalty function method with global convergence properties for nonlinear programming problems, Math. Program. 36(1986), 1-18 44 R. Fandom Noubiap
On the Role of the Mangasarian-Fromovitz Constraint.. - Guddat, Guerra, Nowack (1997) (2 citations) (Correct)
.... is a stationary point for P 1 (1) then x is a stationary point for (P ) b) If x is a stationary point for (P ) then there exist vectors v 2 IR m ; w 2 IR s , such that (x; v; w) is a stationary point for P 1 (1) 2 Secondly, we consider the so called exact penalty methods proposed e.g. in [14] for problems without equality constraints (i.e. I = We propose the following embedding (cf. M 5 (t) in [2] P 2 (t) minfF 2 (x; w; t) j (x; w) 2 M 2 (t)g; t 2 [0; 1] where F 2 (x; w; t) F (A;B;x 0 ;w 0 ;w 1 ;d) x; w; t) tf(x) 1 Gamma t) X j2J j (x) w j Gamma w 0 ....
.... problem (P ) ensuring that the MFCQ is satisfied for all (x; v; w) 2 M 1 (t) x; w) 2 M 2 (t) and (x; v; w; 2 M 3 (t) for all t 2 [0; 1] We discuss the so called Enlarged Mangasarian Fromovitz Constraint Qualification (briefly EnMFCQ) introduced in 1985 in [5] and, simultaneously in [14] in a modified version, later on used in [8] 6] 2] and in further papers of di Pillo, Grippo et al. Definition 3.1 Assume (B1) and p p (cf. B2) The EnMFCQ is satisfied if, for each x 2 E(p) a) D x h i (x) i 2 I, are linearly independent, b) there exists a vector 2 IR n with h ....
Di Pillo, G., Grippo, L. (1986): An exact penalty function method with global convergence properties for nonlinear programming. Math. Programming, 36, 1-18.
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