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

Abstract

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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.


How to cite

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El 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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  1. A. El Afia, A. Benchakroun, and J.-P. Dussault, Asymptotic Analysis of the trajectories of the logarithmic barrier Algogarith without differentiable objective function, IJPAM9 (2003) 99–123.  Zbl1087.90071
  2. A. El afia, Comportement de la barrière logarithmique au voisinage d'une solution dégénérée. Thèse de doctorat, Université de Sherbrooke, Sherbrooke (1999).  
  3. C.G. Broyden and N.F. Attia, Penalty functions, Newton's method, and quadratic Programming. J. Optim. Theor. Appl.58 (1988) 377–381.  Zbl0628.90056
  4. J.-P. Dussault, Numerical Stability and Efficiency of Penality Algorithms. 32 (1995) 296–317.  Zbl0816.65039
  5. 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).  
  6. A.V. Fiacco and G.P. McCormick, Nonlinear Programming: Sequential Unconstrained Minimization Techniques, SIAM, Philadelphia (1990).  
  7. F. John, Extremum problems with inequalities as subsidiary conditions, in: Studies and essays: Courant anniversary volume, Interscience, New York (1948) 187–204.  
  8. 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.  
  9. R. Mifflin, Convergence Bounds For Nonlinear Programming Algorithms. Math. Program.8 (1975) 251–271.  Zbl0326.90055

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