Asymptotic analysis of the trajectories of the logarithmic barrier algorithm without constraint qualifications
A. El Afia; A. Benchakroun; J.-P. Dussault; K. El Yassini
RAIRO - Operations Research (2008)
- Volume: 42, Issue: 2, page 157-198
- ISSN: 0399-0559
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topEl Afia, A., et al. "Asymptotic analysis of the trajectories of the logarithmic barrier algorithm without constraint qualifications." RAIRO - Operations Research 42.2 (2008): 157-198. <http://eudml.org/doc/250279>.
@article{ElAfia2008,
abstract = {
In this paper, we study the differentiability of the trajectories of the logarithmic barrier algorithm for a nonlinear
program when the set Λ* of the Karush-Kuhn-Tucker multiplier vectors is empty
owing to the fact that the constraint qualifications are not satisfied.
},
author = {El Afia, A., Benchakroun, A., Dussault, J.-P., El Yassini, K.},
journal = {RAIRO - Operations Research},
keywords = {Logarithmic barrier; Penalty algorithms.; logarithmic barrier; penalty algorithms},
language = {eng},
month = {5},
number = {2},
pages = {157-198},
publisher = {EDP Sciences},
title = {Asymptotic analysis of the trajectories of the logarithmic barrier algorithm without constraint qualifications},
url = {http://eudml.org/doc/250279},
volume = {42},
year = {2008},
}
TY - JOUR
AU - El Afia, A.
AU - Benchakroun, A.
AU - Dussault, J.-P.
AU - El Yassini, K.
TI - Asymptotic analysis of the trajectories of the logarithmic barrier algorithm without constraint qualifications
JO - RAIRO - Operations Research
DA - 2008/5//
PB - EDP Sciences
VL - 42
IS - 2
SP - 157
EP - 198
AB -
In this paper, we study the differentiability of the trajectories of the logarithmic barrier algorithm for a nonlinear
program when the set Λ* of the Karush-Kuhn-Tucker multiplier vectors is empty
owing to the fact that the constraint qualifications are not satisfied.
LA - eng
KW - Logarithmic barrier; Penalty algorithms.; logarithmic barrier; penalty algorithms
UR - http://eudml.org/doc/250279
ER -
References
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- J.-P. Dussault, Numerical Stability and Efficiency of Penality Algorithms. 32 (1995) 296–317.
- A.V. Fiacco and G.P. McCormick, Programming under Nonlinear Constraints by Unconstrained Minimization: A Primal-Dual Method, Technical Paper RACTR-96, Research Analysis Corporation, Mc Lean, Va. (1963).
- A.V. Fiacco and G.P. McCormick, Nonlinear Programming: Sequential Unconstrained Minimization Techniques, SIAM, Philadelphia (1990).
- F. John, Extremum problems with inequalities as subsidiary conditions, in: Studies and essays: Courant anniversary volume, Interscience, New York (1948) 187–204.
- H.W. Kuhn and A.W. Tucker, Non-Linear Programming, in Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, edited by J. Neyman, University of California Press, Berkeley (1951) 481–493.
- R. Mifflin, Convergence Bounds For Nonlinear Programming Algorithms. Math. Program.8 (1975) 251–271.
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