Geodesic
A descent method with inexact linear search for nonsmooth equilibrium problems
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 10, pp. 1812-1818 
I. V. Konnov; O. V. Pinyagina. A descent method with inexact linear search for nonsmooth equilibrium problems. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 10, pp. 1812-1818. http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_10_a4/
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     title = {A descent method with inexact linear search for nonsmooth equilibrium problems},
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Voir la notice de l'article provenant de la source Math-Net.Ru

A descent method with respect to the gap function is formulated and justified for the nonsmooth equilibrium problem. It uses the procedure of inexact linear search of the Armijo type. The proposed method converges under the same assumptions as the methods with exact linear search.

[1] Baiokki K., Kapelo A., Variatsionnye i kvazivariatsionnye neravenstva. Prilozheniya k zadacham so svobodnoi granitsei, Nauka, M., 1988 | MR

[2] Blum E., Oettli W., “From optimization and variational inequalities to equilibrium problems”, Math. Student., 63:1 (1994), 123–145 | MR | Zbl

[3] Konnov I. V., Generalized monotone equilibrium problems and variational inequalities. Handbook of generalized convexity and generalized monotonicity, Springer, New York, 2005, 559–618 pp. | MR

[4] Patrikssoon M., Nonlinear programming and variational inequality problems: a unified approach, Kluwer Acad. Publ., Dordrecht, 1999 | MR

[5] Konnov I. V., Pinyagina O. V., “D-gap functions for a class of general equilibrium problems in Banach spaces”, Comput. Meth. Appl. Math., 3:2 (2003), 274–286 | MR | Zbl

[6] Konnov I. V., Pinyagina O. B., “Metod spuska po intervalnoi funktsii dlya negladkikh zadach ravnovesiya”, Izv. vuzov. Matematika, 2003, no. 12, 71–77 | MR | Zbl

[7] Demyanov V. F., Rubinov A. I., Osnovy negladkogo analiza i kvazidifferentsialnoe ischislenie, Nauka, M., 1990 | MR