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See detailLocal convergence of quasi-Newton methods under metric regularity
Aragón Artacho, Francisco Javier UL; Belyakov, A.; Dontchev, A. L. et al

in Computational Optimization and Applications (2014), 58(1), 225-247

We consider quasi-Newton methods for generalized equations in Banach spaces under metric regularity and give a sufficient condition for q-linear convergence. Then we show that the well-known Broyden ... [more ▼]

We consider quasi-Newton methods for generalized equations in Banach spaces under metric regularity and give a sufficient condition for q-linear convergence. Then we show that the well-known Broyden update satisfies this sufficient condition in Hilbert spaces. We also establish various modes of q-superlinear convergence of the Broyden update under strong metric subregularity, metric regularity and strong metric regularity. In particular, we show that the Broyden update applied to a generalized equation in Hilbert spaces satisfies the Dennis–Moré condition for q-superlinear convergence. Simple numerical examples illustrate the results. [less ▲]

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See detailA Lyusternik - Graves theorem for the proximal point method
Aragón Artacho, Francisco Javier UL; Gaydu, M.

in Computational Optimization and Applications (2012), 52(3), 785-803

We consider a generalized version of the proximal point algorithm for solving the perturbed inclusion y∈T(x), where y is a perturbation element near 0 and T is a set-valued mapping acting from a Banach ... [more ▼]

We consider a generalized version of the proximal point algorithm for solving the perturbed inclusion y∈T(x), where y is a perturbation element near 0 and T is a set-valued mapping acting from a Banach space X to a Banach space Y which is metrically regular around some point (x̅,0) in its graph. We study the behavior of the convergent iterates generated by the algorithm and we prove that they inherit the regularity properties of T, and vice versa. We analyze the cases when the mapping T is metrically regular and strongly regular. [less ▲]

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See detailScheduling with uncertainties on new computing platforms
Mahjoub, Amine; Pecero, Johnatan UL; Trystram, Denis

in Computational Optimization and Applications (2010), 48(2), 369-398

New distributed computing platforms (grids) are based on interconnections of a large number of processing elements. A most important issue for their effective utilization is the optimal use of resources ... [more ▼]

New distributed computing platforms (grids) are based on interconnections of a large number of processing elements. A most important issue for their effective utilization is the optimal use of resources through proper task scheduling. It consists of allocating the tasks of a parallel program to processors on the platform and to determine at what time the tasks will start their execution. As data may be subject to uncertainties or disturbances, it is practically impossible to precisely predict the input parameters of the task scheduling problem. We briefly survey existing approaches for dealing with data uncertainties and discuss their relevance in the context of grid computing. We describe the stabilization process and analyze a scheduling algorithm that is intrinsically stable (i.e., it mitigates the effects of disturbances in input data at runtime). This algorithm is based on a decomposition of the application graph into convex sets of vertices. Finally, it is compared experimentally to pure on-line and well-known off-line algorithms. [less ▲]

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