This paper studies convergence properties of inexact variants of the proximal point algorithm when applied to a certain class of nonmonotone mappings. The presented algorithms allow for constant relative errors, in the line of the recently proposed hybrid proximal-extragradient algorithm. The main convergence result extends a recent work of the second author, where exact solutions for the proxi...

The global attractivity of the positive steady state is established for a class of nonmonotone time-delayed reaction-diffusion equations subject to the Neumann boundary condition via a fluctuation method. This result is also applied to three population models.

A visual search has been made of four fields using United Kingdom 1.2m Schmidt Objective Prism plates with a reciprocal dispersion of 1 180 A/mm at HP. Such plate material is ideally suited to searches for emission-line galaxies. We present a catalogue of 53 emission-line objects, which comprises 45 galaxies, where individual HI1 regions are resolved in 16 bright galaxies; 8 are emission li...

We propose and analyze a class of penalty-function-free nonmonotone trust-region methods for nonlinear equality constrained optimization problems. The algorithmic framework yields global convergence without using a merit function and allows nonmonotonicity independently for both, the constraint violation and the value of the Lagrangian function. Similar to the Byrd–Omojokun class of algorithms,...

We consider a generalization of the gradient method with retards for the solution of large-scale unconstrained optimization problems. Recently, the gradient method with retards was introduced to find global minimizers of large-scale quadratic functions. The most interesting feature of this method is that it does not involve a decrease in the objective function, which allows fast local convergen...

In this paper, we present a nonmonotone trust-region method of conic model for unconstrained optimization. The new method combines a new trust-region subproblem of conic model proposed in [Y. Ji, S.J. Qu, Y.J. Wang, H.M. Li, A conic trust-region method for optimization with nonlinear equality and inequality 4 constrains via active-set strategy, Appl. Math. Comput. 183 (2006) 217–231] with a non...

We consider equation ut(t, x) = ∆u(t, x)−u(t, x)+g(u(t−h, x)) (∗), when g : R+ → R+ has exactly two fixed points: x1 = 0 and x2 = κ > 0. Assuming that g is unimodal and has negative Schwarzian, we indicate explicitly a closed interval C = C(h, g(0), g(κ)) = [c∗, c] such that (∗) has at least one (possibly, nonmonotone) travelling front propagating at velocity c for every c ∈ C. Here c∗ > 0 is f...