Asymptotic analysis of the trajectories of the logarithmic barrier algorithm without constraint qualifications
RAIRO - Operations Research - Recherche Opérationnelle, Tome 42 (2008) no. 2, pp. 157-198.

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.

DOI : 10.1051/ro:2008008
Classification : 90C30
Mots-clés : logarithmic barrier, penalty algorithms 
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     author = {Afia, A. El and Benchakroun, A. and Dussault, J.-P. and Yassini, K. El},
     title = {Asymptotic analysis of the trajectories of the logarithmic barrier algorithm without constraint qualifications},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {157--198},
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Afia, A. El; Benchakroun, A.; Dussault, J.-P.; Yassini, K. El. Asymptotic analysis of the trajectories of the logarithmic barrier algorithm without constraint qualifications. RAIRO - Operations Research - Recherche Opérationnelle, Tome 42 (2008) no. 2, pp. 157-198. doi : 10.1051/ro:2008008. http://archive.numdam.org/articles/10.1051/ro:2008008/

[1] A. El Afia, A. Benchakroun, and J.-P. Dussault, Asymptotic Analysis of the trajectories of the logarithmic barrier Algogarith without differentiable objective function, IJPAM 9 (2003) 99-123. | MR | Zbl

[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. | MR | Zbl

[4] J.-P. Dussault, Numerical Stability and Efficiency of Penality Algorithms. 32 (1995) 296-317. | MR | Zbl

[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). | MR | Zbl

[7] F. John, Extremum problems with inequalities as subsidiary conditions, in: Studies and essays: Courant anniversary volume, Interscience, New York (1948) 187-204. | MR | Zbl

[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. | MR | Zbl

[9] R. Mifflin, Convergence Bounds For Nonlinear Programming Algorithms. Math. Program. 8 (1975) 251-271. | MR | Zbl

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