The Idempotent Analog of Resolvent Kernels for a Deterministic Optimal Control Problem

Idempotent Analogue of Resolvent Kernels for a Deterministic Optimal Control Problem

An object oriented approach to idempotent analysis: Integral Equations as Optimal Control Problems

Within the framework of generic programming, we implement an abstract algorithm for solution of an integral equation of second kind with the resolvent kernels method. Then, as an application of the idempotent analysis analog of resolvent kernels developed in [LP01], we apply the algorithm to the numerical solution of an optimal control problem with stopping time. 1991 Mathematics Subject Classi...

On supermatrix idempotent operator semigroups

One-parameter semigroups of antitriangle idempotent supermatrices and corresponding superoperator semigroups are introduced and investigated. It is shown that t-linear idempotent superoperators and exponential superoperators are mutually dual in some sense, and the first gives additional to exponential solution to the initial Cauchy problem. The corresponding functional equation and analog of r...

Stability Analysis and Optimal Control of Vaccination and Treatment of a SIR Epidemiological Deterministic Model with Relapse

In this paper, we studied and formulated the relapsed SIR model of a constant size population with standard incidence rate. Also, the optimal control problem with treatment and vaccination as controls, subject to the model is formulated. The analysis carried out on the model, clearly showed that the infection free steady state is globally asymptotically stable if the bas...

A Hybrid Proximal Point Algorithm for Resolvent operator in Banach Spaces

Equilibrium problems have many uses in optimization theory and convex analysis and which is why different methods are presented for solving equilibrium problems in different spaces, such as Hilbert spaces and Banach spaces. The purpose of this paper is to provide a method for obtaining a solution to the equilibrium problem in Banach spaces. In fact, we consider a hybrid proximal point algorithm...