Wendler, K. (1993) Implementation of a pathfollowing procedure for solving nonlinear one-parametric optimization problems. In: Brosowski, B. et al (eds) Multicriteria decision, in Ser approximation and optimization, Verlag Peter Lang Frankfurt am Main, Berlin, Bern, New York, Paris, Wien 139-163.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....constraints as inequalities constraints. In Chapter 4 we propose JJT and KH regular versions of the above embeddings. Furthermore, the role of the EnMFCQ is cleared. Chapter 5 gives a summary of conclusions and further remarks. All illustrative examples were generated on the computer by PAFO ([25], 12] Acknowledgements The author thanks J. Guddat for stimulating discussions on the subject of this paper. 2 Theoretical Background We consider the one parametric optimization problem P(t) minff(x; t) x 2 M(t)g; t 2 IR; where M(t) fx 2 IR n =h i (x; t) 0; i 2 I; g j (x; t) 0; j 2 ....

Wendler, K. (1993) Implementation of a pathfollowing procedure for solving nonlinear one-parametric optimization problems. In: Brosowski, B. et al (eds) Multicriteria decision, in Ser approximation and optimization, Verlag Peter Lang Frankfurt am Main, Berlin, Bern, New York, Paris, Wien 139-163.

....stability result given in [13] Theorem 2.8 (cf. 13] We assume (C1) and (C4) Then M(t 1 ) is homeomorphic with M(t 2 ) for all t 1 ; t 2 2 [0; 1] 2 10 Multiobjective optimization: embeddings On the program package PAFO (this is a very short version of 4.5 and 5. 2 in [12] PAFO (cf. [19] and [5] is based on a pathfollowing method (called PATH III in 4.5 [12] and jumps (called JUMP I in 5.2 [12] and JUMP II in 5.3 [12] We explain the main ideas of PATH III and JUMP I, but not those of JUMP II as we do not need them here. PATH III This algorithm computes a numerical ....

Wendler, K. (1993): Implementation of a Pathfollowing Procedure for Solving Nonlinear One-Parametric Optimization Problems. In: Brosowski, B. et al. (eds.) Multicriteria Decision. In: Ser. Approximation and Optimization. Verlag Peter Lang, Frankfurt a.M., Berlin, Bern, New York, Paris, Wien, 139-163.

....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 ....

....j (x; t) d j 0; j 2 J ) is KH regular. 2 Now, we present some facts about pathfollowing methods (for more details see [8] For this, we assume (A1) A2) and the JJT regularity of the considered problem P (t) The algorithm PATH III the corresponding computer program is called PAFO (cf. [8, 7, 16]) computes a numerical description of a compact connected component in Sigma gc and Sigma stat , respectively. In the last part of Chapter 2 we present two theorems that are essential for our analysis. Theorem 2.5 ( 5] We assume (C1) M(t) is non empty and there exists a compact set C with ....

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Wendler, K. (1993): Implementation of a pathfollowing procedure for solving nonlinear one-parametric optimization problems. In: Brosowski, B. et al. (eds.) Multicriteria decision. In: Ser. approximation and optimization. Verlag Peter Lang, Frankfurt a.M., Berlin, Bern, New York, Paris, Wien, 139-163.

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