This paper presents a variant of logarithmic penalty methods for nonlinear convex programming. If the descent direction is obtained through a classical Newton-type method, the line search is done on a majorant function. Numerical tests show the efficiency of this approach versus classical line searches.
Accepté le :
DOI : 10.1051/ro/2018061
Mots-clés : Logarithmic penalty method, method of majorant functions, convex programming
@article{RO_2019__53_1_29_0, author = {Bachir Cherif, Larbi and Merikhi, Bachir}, title = {A penalty method for nonlinear programming}, journal = {RAIRO - Operations Research - Recherche Op\'erationnelle}, pages = {29--38}, publisher = {EDP-Sciences}, volume = {53}, number = {1}, year = {2019}, doi = {10.1051/ro/2018061}, zbl = {1414.90264}, mrnumber = {3899028}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/ro/2018061/} }
TY - JOUR AU - Bachir Cherif, Larbi AU - Merikhi, Bachir TI - A penalty method for nonlinear programming JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2019 SP - 29 EP - 38 VL - 53 IS - 1 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ro/2018061/ DO - 10.1051/ro/2018061 LA - en ID - RO_2019__53_1_29_0 ER -
%0 Journal Article %A Bachir Cherif, Larbi %A Merikhi, Bachir %T A penalty method for nonlinear programming %J RAIRO - Operations Research - Recherche Opérationnelle %D 2019 %P 29-38 %V 53 %N 1 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ro/2018061/ %R 10.1051/ro/2018061 %G en %F RO_2019__53_1_29_0
Bachir Cherif, Larbi; Merikhi, Bachir. A penalty method for nonlinear programming. RAIRO - Operations Research - Recherche Opérationnelle, Tome 53 (2019) no. 1, pp. 29-38. doi : 10.1051/ro/2018061. http://archive.numdam.org/articles/10.1051/ro/2018061/
[1] Interior point methods in semi-definite programming with application to combinatorial optimization. SIAM J. Optimiz. 5 (1995) 13–55. | DOI | MR | Zbl
,[2] Numerical optimization: theoretical and practical aspects. Mathematics and Applications, Vol. 27. Springer-Verlag, Berlin (2003). | MR | Zbl
, , and ,[3] A logarithm barrier method for semi-definite programming. RAIRO: OR 42 (2008) 123–139. | DOI | Numdam | MR | Zbl
, ,[4] New bounds for the extreme values of a finite sample of real numbers, J. Math. Anal. Appl. 197 (1996) 411–426. | DOI | MR | Zbl
and ,[5] Extension de quelques méthodes de points intérieurs pour la programmation semi-definie. These de doctorat, Universite de Setif (2006).
,[6] Résolution de problèmes non linéaires par les méthodes de points intérieurs. Théorie et algorithmes. These de doctorat, Universite du Havre, France (2006).
,[7] A mathematical theory of communication, Bell Syst. Tech. J. 27 (1948) 379–423 and 623–656. | DOI | MR | Zbl
,[8] Bounds for eigenvalues using traces. Linear Algebra Appl. 29 (1980) 471–506. | DOI | MR | Zbl
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