A new active set algorithm (ASA) for large-scale box constrained optimization is introduced. The algorithm consists of a nonmonotone gradient projection step, an unconstrained optimization step, and a set of rules for switching between the two steps. Numerical experiments and comparisons are presented using box constrained problems in the CUTEr and MINPACK test problem libraries. keywords: Nonm...

In this paper we propose new globalization strategies for the Barzilai and Borwein gradient method, based on suitable relaxations of the monotonicity requirements. In particular, we define a class of algorithms that combine nonmonotone watchdog techniques with nonmonotone linesearch rules and we prove the global convergence of these schemes. Then we perform an extensive computational study, whi...

Nonmonotone gradient methods generally perform better than their monotone counterparts especially on unconstrained quadratic optimization. However, the known convergence rate of method is often much its nonmonotone variant. With aim shrinking gap between theory and practice methods, we introduce a property for analysis large collection methods. We prove that any using stepsizes satisfying will ...

In this paper a fully dynamic viscoelastic contact problem is studied. The contact is assumed to be bilateral and frictional, where the friction law is described by a nonmonotone relation between the tangential stress and the tangential velocity. A weak formulation of the problem leads to a second order nonmonotone subdifferential inclusion, also known as a second order hyperbolic hemivariation...

We describe recent existence and uniqueness results obtained for nonlocal nonmonotone Eikonal equations modelling the evolution of interfaces. We focus on two model cases. The first one arises in dislocation dynamics and the second one comes from a FitzHughNagumo system. The equation is nonlocal since, in both case, the velocity at a point of the boundary of the interface depends on the whole e...

In this paper, we present nonmonotone methods for feedforward neural network training, i.e. training methods in which error function values are allowed to increase at some iterations. More specifically, at each epoch we impose that the current error function value must satisfy an Armijo-type criterion, with respect to the maximum error function value of M previous epochs. A strategy to dynamica...