Geodesic
A modified standard embedding for linear complementarity problems
Kybernetika, Tome 40 (2004) no. 5, p. [551]

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

We propose a modified standard embedding for solving the linear complementarity problem (LCP). This embedding is a special one-parametric optimization problem $P(t), t \in [0,1]$. Under the conditions (A3) (the Mangasarian–Fromovitz Constraint Qualification is satisfied for the feasible set $M(t)$ depending on the parameter $t$), (A4) ($P(t)$ is Jongen–Jonker– Twilt regular) and two technical assumptions, (A1) and (A2), there exists a path in the set of stationary points connecting the chosen starting point for $P(0)$ with a certain point for $P(1)$ and this point is a solution for the (LCP). This path may include types of singularities, namely points of Type 2 and Type 3 in the class of Jongen–Jonker–Twilt for $t\in [0,1)$. We can follow this path by using pathfollowing procedures (included in the program package PAFO). In case that the condition (A3) is not satisfied, also points of Type 4 and 5 may appear. The assumption (A4) will be justified by a perturbation theorem. Illustrative examples are presented.
Classification : 68Q25, 90C31, 90C33, 90C51
Keywords: linear complementarity problem; standard embedding; Jongen– Jonker–Twilt regularity; Mangasarian–Fromovitz constraint qualification; pathfollowing methods 
@article{KYB_2004__40_5_a2,
     author = {Allonso, Sira Allende and Guddat, J\"urgen and Nowack, Dieter},
     title = {A modified standard embedding for linear complementarity problems},
     journal = {Kybernetika},
     pages = {[551]},
     publisher = {mathdoc},
     volume = {40},
     number = {5},
     year = {2004},
     mrnumber = {2120996},
     zbl = {1249.90273},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2004__40_5_a2/}
}
TY  - JOUR
AU  - Allonso, Sira Allende
AU  - Guddat, Jürgen
AU  - Nowack, Dieter
TI  - A modified standard embedding for linear complementarity problems
JO  - Kybernetika
PY  - 2004
SP  - [551]
VL  - 40
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/KYB_2004__40_5_a2/
LA  - en
ID  - KYB_2004__40_5_a2
ER  - 
%0 Journal Article
%A Allonso, Sira Allende
%A Guddat, Jürgen
%A Nowack, Dieter
%T A modified standard embedding for linear complementarity problems
%J Kybernetika
%D 2004
%P [551]
%V 40
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/KYB_2004__40_5_a2/
%G en
%F KYB_2004__40_5_a2
Allonso, Sira Allende; Guddat, Jürgen; Nowack, Dieter. A modified standard embedding for linear complementarity problems. Kybernetika, Tome 40 (2004) no. 5, p. [551]. http://geodesic.mathdoc.fr/item/KYB_2004__40_5_a2/