scholarly journals Controlling heroin addiction via age-structured modeling

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Anwarud Din ◽  
Yongjin Li
Keyword(s):  
Maximum Principle ◽  
Age Structure ◽  
Control Variable ◽  
Adjoint Equations ◽  
Heroin Addiction ◽  
Heroin Users ◽  
The Maximum Principle ◽  
Optimal Value ◽  
Age Structured ◽  
Weak Derivatives

Abstract The aim of the present study is to consider a heroin epidemic model with age-structure only in the active heroin users. The model was formulated with the help of available literature on heroin epidemic. Instead of treatment as a class, we incorporated recovered population and considered treatment as a control variable and thus a control problem is presented for further analysis. The techniques of weak derivatives and sensitivities were used for obtaining the adjoint equations. The maximum principle of Pontryagin’ type was used for obtaining the optimal value of the control variable. Sample simulations are presented at the end of the study in order to show the effectiveness of the treatment.

scholarly journals Stochastic Maximum Principle for Partial Information Optimal Control Problem of Forward-Backward Systems Involving Classical and Impulse Controls

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Yan Wang ◽  
Aimin Song ◽  
Enmin Feng
Keyword(s):  
Maximum Principle ◽  
Impulse Control ◽  
Optimization Problem ◽  
Partial Information ◽  
Control Variable ◽  
Necessary Optimality Conditions ◽  
Explicit Solutions ◽  
The Maximum Principle ◽  
Portfolio Optimization Problem ◽  
Impulse Controls

We study the partial information classical and impulse controls problem of forward-backward systems driven by Lévy processes, where the control variable consists of two components: the classical stochastic control and the impulse control; the information available to the controller is possibly less than the full information, that is, partial information. We derive a maximum principle to give the sufficient and necessary optimality conditions for the local critical points of the classical and impulse controls problem. As an application, we apply the maximum principle to a portfolio optimization problem with piecewise consumption processes and give its explicit solutions.

Stochastic maximum principle, dynamic programming principle, and their relationship for fully coupled forward-backward stochastic controlled systems

2020 ◽  
Vol 26 ◽  
pp. 81
Author(s):  
Mingshang Hu ◽  
Shaolin Ji ◽  
Xiaole Xue
Keyword(s):  
Dynamic Programming ◽  
Maximum Principle ◽  
Adjoint Equations ◽  
Dynamic Programming Principle ◽  
The Maximum Principle ◽  
Controlled Systems ◽  
Local Case ◽  
Hamilton Jacobi Bellman ◽  
The Relationship ◽  
Fully Coupled

Within the framework of viscosity solution, we study the relationship between the maximum principle (MP) from M. Hu, S. Ji and X. Xue [SIAM J. Control Optim. 56 (2018) 4309–4335] and the dynamic programming principle (DPP) from M. Hu, S. Ji and X. Xue [SIAM J. Control Optim. 57 (2019) 3911–3938] for a fully coupled forward–backward stochastic controlled system (FBSCS) with a nonconvex control domain. For a fully coupled FBSCS, both the corresponding MP and the corresponding Hamilton–Jacobi–Bellman (HJB) equation combine an algebra equation respectively. With the help of a new decoupling technique, we obtain the desirable estimates for the fully coupled forward–backward variational equations and establish the relationship. Furthermore, for the smooth case, we discover the connection between the derivatives of the solution to the algebra equation and some terms in the first-order and second-order adjoint equations. Finally, we study the local case under the monotonicity conditions as from J. Li and Q. Wei [SIAM J. Control Optim. 52 (2014) 1622–1662] and Z. Wu [Syst. Sci. Math. Sci. 11 (1998) 249–259], and obtain the relationship between the MP from Z. Wu [Syst. Sci. Math. Sci. 11 (1998) 249–259] and the DPP from J. Li and Q. Wei [SIAM J. Control Optim. 52 (2014) 1622–1662].

scholarly journals Stochastic maximum principle for optimal control problem of forward and backward system

1995 ◽  
Vol 37 (2) ◽  
pp. 172-185 ◽  
Author(s):  
Wensheng Xu
Keyword(s):  
Optimal Control ◽  
Diffusion Coefficient ◽  
Maximum Principle ◽  
Optimal Control Problem ◽  
Stochastic Systems ◽  
Optimal Control Problems ◽  
Control Variable ◽  
Control Problems ◽  
State Variables ◽  
The Maximum Principle

AbstractThe maximum principle for optimal control problems of stochastic systems consisting of forward and backward state variables is proved, under the assumption that the diffusion coefficient does not contain the control variable, but the control domain need not be convex.

scholarly journals Local versus nonlocal elliptic equations: short-long range field interactions

2020 ◽  
Vol 10 (1) ◽  
pp. 895-921
Author(s):  
Daniele Cassani ◽  
Luca Vilasi ◽  
Youjun Wang
Keyword(s):  
Asymptotic Behavior ◽  
Maximum Principle ◽  
Weak Solutions ◽  
Elliptic Equations ◽  
Spectral Properties ◽  
Fractional Laplacian ◽  
Coupling Parameter ◽  
Nonlocal Operators ◽  
The Maximum Principle ◽  
Regularity Results

Abstract In this paper we study a class of one-parameter family of elliptic equations which combines local and nonlocal operators, namely the Laplacian and the fractional Laplacian. We analyze spectral properties, establish the validity of the maximum principle, prove existence, nonexistence, symmetry and regularity results for weak solutions. The asymptotic behavior of weak solutions as the coupling parameter vanishes (which turns the problem into a purely nonlocal one) or goes to infinity (reducing the problem to the classical semilinear Laplace equation) is also investigated.

scholarly journals Regularized Asymptotics of the Solution of the Singularly Perturbed First Boundary Value Problem on the Semiaxis for a Parabolic Equation with a Rational “Simple” Turning Point

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 405
Author(s):  
Alexander Yeliseev ◽  
Tatiana Ratnikova ◽  
Daria Shaposhnikova
Keyword(s):  
Parabolic Equation ◽  
Maximum Principle ◽  
Boundary Value Problem ◽  
Regularization Method ◽  
Turning Point ◽  
Boundary Value ◽  
Singularly Perturbed ◽  
Asymptotic Convergence ◽  
The Maximum Principle ◽  
Regularized Asymptotics

The aim of this study is to develop a regularization method for boundary value problems for a parabolic equation. A singularly perturbed boundary value problem on the semiaxis is considered in the case of a “simple” rational turning point. To prove the asymptotic convergence of the series, the maximum principle is used.

Optimal Control of a General Environmental Space

1986 ◽  
Vol 108 (4) ◽  
pp. 330-339 ◽  
Author(s):  
M. A. Townsend ◽  
D. B. Cherchas ◽  
A. Abdelmessih
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Moisture Content ◽  
Control Strategies ◽  
Switching Control ◽  
The Maximum Principle ◽  
Environmental Space ◽  
And Performance

This study considers the optimal control of dry bulb temperature and moisture content in a single zone, to be accomplished in such a way as to be implementable in any zone of a multi-zone system. Optimality is determined in terms of appropriate cost and performance functions and subject to practical limits using the maximum principle. Several candidate optimal control strategies are investigated. It is shown that a bang-bang switching control which is theoretically periodic is a least cost practical control. In addition, specific attributes of this class of problem are explored.

ASYMPTOTIC DECAY TOWARD THE PLANAR RAREFACTION WAVES FOR A MODEL SYSTEM OF THE RADIATING GAS IN TWO DIMENSIONS

2008 ◽  
Vol 18 (04) ◽  
pp. 511-541 ◽  
Author(s):  
WENLIANG GAO ◽  
CHANGJIANG ZHU
Keyword(s):  
Cauchy Problem ◽  
Maximum Principle ◽  
Coupled System ◽  
Model System ◽  
Two Dimensions ◽  
Rarefaction Waves ◽  
Asymptotic Decay ◽  
The Maximum Principle ◽  
The Cauchy Problem ◽  
Asymptotic Decay Rate

In this paper, we consider the asymptotic decay rate towards the planar rarefaction waves to the Cauchy problem for a hyperbolic–elliptic coupled system called as a model system of the radiating gas in two dimensions. The analysis based on the standard L2-energy method, L1-estimate and the monotonicity of profile obtained by the maximum principle.

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