Jongen, H.Th., Jonker, P., Twilt, F. (1986): On One-Parametric Families of Optimization Problems. Equality Constraints. JOTA 48, 141-161. Home/Search Document Not in Database Summary Related Articles Check |
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New embeddings for nonlinear multiobjective optimization.. - Guddat, GUERRA, NOWACK (1998) (Correct)
....Furthermore, it is shown that if 0 2 IR n m s is a regular value of H, then the set H Gamma1 (0) is a piecewise one dimensional C 1 manifold (briefly PC 1 manifold) Next, we cite our short characterization from 2. 5 in [12] of the class F introduced by Jongen, Jonker and Twilt ([15, 16]) In [16] the local structure of Sigma gc is completely 1 For the definition we refer to [16] see [12] too 2 We consider the gradient D x h i (x; t) as a row vector. 6 Multiobjective optimization: embeddings described if (f; H;G) belongs to a C 3 s open and dense subset F of C 3 ....
Jongen, H.Th., Jonker, P., Twilt, F. (1986): On One-Parametric Families of Optimization Problems. Equality Constraints. JOTA 48, 141-161.
On the Role of the Mangasarian-Fromovitz Constraint.. - Guddat, Guerra, Nowack (1997) (2 citations) (Correct)
....c(t) t 1 Gamma t tends to 1 if t tends to 1. This one parametric optimization problem has the following disadvantages: The problem is not defined for t = 1, the objective function is exactly once continuously differentiable (i.e. the results of parametric optimization presented in [8, 9, 10, 11, 12, 13, 15, 16, 7] a short summary is given in Chapter 2 are not applicable) we do not know any starting point for t = 0. It is easy to see that these disadvantages will not appear for P 1 (t) Moreover, there are further important properties of P 1 (t) cf. Theorem 1.1) The term (1 Gamma t) x Gamma x 0 ....
....continuously differentiable functions. Furthermore, it is shown that if 0 2 IR n m s is a regular value of H, then the set H Gamma1 (0) is a piecewise one dimensional C 1 manifold. Next, we cite our short characterization from [2] of the class F introduced by Jongen, Jonker and Twilt ([11, 12]) In [12] the local structure of Sigma gc is completely described if (f; H;G) belongs to a C 3 s open and dense subset F of C 3 (IR n Theta IR; IR) 1 m s , where C 3 s denotes the strong (or Whitney ) C 3 topology. If (f; H;G) 2 F , then Sigma gc can be divided into 5 types. ....
Jongen, H.Th., Jonker, P., Twilt, F. (1986): On one-parametric families of optimization problems. Equality constraints. JOTA 48, 141-161.
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