Convergence of the steepest descent method with line searches and uniformly convex objective in reflexive Banach spaces
Gallego, Fernando Andrés ; Quintero, John Jairo ; Riano, Juan Carlos
Mathematical Communications, Tome 20 (2015) no. 1, p. 161-173 / Harvested from Mathematical Communications
Text on Mathematical Communications
In this paper, we present some algorithms for unconstrained convex optimization problems. The development and analysis of these methods is carried out in a Banach space setting. We begin by introducing a general framework for achieving global convergence without Lipschitz conditions on the gradient, as usual in the current literature. This paper is an extension to Banach spaces to the analysis of the steepest descent method for convex optimization, most of them in less general spaces.
Publié le : 2015-11-08
Classification:  uniformly convex functional, descent methods, step-size estimation, metric of gradient,  90C25; 49M29; 46N10; 46N40 
@article{mc685,
     author = {Gallego, Fernando Andr\'es and Quintero, John Jairo and Riano, Juan Carlos},
     title = {Convergence of the steepest descent method with line searches and uniformly convex objective in reflexive Banach spaces},
     journal = {Mathematical Communications},
     volume = {20},
     number = {1},
     year = {2015},
     pages = { 161-173},
     language = {eng},
     url = {http://dml.mathdoc.fr/item/mc685}
}

Gallego, Fernando Andrés; Quintero, John Jairo; Riano, Juan Carlos. Convergence of the steepest descent method with line searches and uniformly convex objective in reflexive Banach spaces. Mathematical Communications, Tome 20 (2015) no. 1, pp.  161-173. http://gdmltest.u-ga.fr/item/mc685/