It was recently shown that, in the solution of smooth constrained optimization problems by sequential quadratic programming (SQP), the Maratos eeect can be prevented by means of a certain nonmonotone (more precisely, three-step or four-step monotone) line search. Using a well known transformation, this scheme can be readily extended to the case of minimax problems. It turns out however that, du...

Classical results in the theory of monotone semiflows give sufficient conditions for the generic solution to converge toward an equilibrium or towards the set of equilibria (quasiconvergence). In this paper, we provide new formulations of these results in terms of the measure-theoretic notion of prevalence, developed in [1, 8]. For monotone reaction-diffusion systems with Neumann boundary condi...

Many models in biology and ecology can be described by reaction-diffusion equations wit time delay. One of important solutions for these type of equations is the traveling wave solution that shows the phenomenon of wave propagation. The existence of traveling wave fronts has been proved for large class of equations, in particular, the monotone systems, such as the cooperative systems and some c...

Symmetries play an important role in the dynamics of physical systems. As example, quantum physics and microworld are basis symmetry principles. These problems reduced to solving inequalities general. That is why this article, we study numerical approximation solutions variational inequality involving quasimonotone operators infinite-dimensional real Hilbert space. We prove that iterative seque...

The single-crossing assumption simplifies the analysis of screening models as local incentive compatibility becomes sufficient for global incentive compatibility. If single crossing is violated, global incentive compatibility constraints have to be taken into account. This paper studies monotone solutions in a screening model that allows a one-time violation of single crossing. The results show...

Often, monotonicity is a desirable property of probabilistic networks. For example, when medical knowledge in a particular domain dictates that more severe symptoms increase the likeliness of a more serious disease, these properties should be reflected in the network. Unfortunately, the problem to determine for a given probabilistic network whether it is monotone is known to be a highly intract...

We consider Pogorelov estimates and Liouville-type theorems to parabolic [Formula: see text]-Hessian equations of the form text] in text]. derive that any text]-convex-monotone solution when satisfies a quadratic growth must be linear function plus polynomial

In this paper an algorithm for approximate solving of a boundary value problem nonlinear differential equation with special type fractional derivative is suggested. This called generalized proportional Caputo derivative. The new based on the application monotone-iterative technique combined method lower and upper solutions. connection this, initially, linear condition studied, its explicit solu...

Abstract The primary goal of this research is to investigate the approximate numerical solution variational inequalities using quasimonotone operators in infinite-dimensional real Hilbert spaces. In study, sequence obtained by proposed iterative technique for solving converges strongly toward a due viscosity-type scheme. Furthermore, new that uses an inertial mechanism obtain strong convergence...

Many AI/Machine learning problems require adaptively selecting a sequence of items, each selected item might provide some feedback that is valuable for making better selections in the future, with goal maximizing an adaptive submodular function. Most existing studies this field focus on either monotone case or non-monotone case. Specifically, if utility function and submodular, Golovin Krause (...