scholarly journals Maximum principle for a nonlinear size-structured model of fish and fry management

2018 ◽  
Vol 23 (4) ◽  
pp. 533-552 ◽  
Author(s):  
Rong Liu ◽  
Guirong Liu
Keyword(s):  
Fixed Point ◽  
Maximum Principle ◽  
Normal Cone ◽  
Necessary Conditions ◽  
Adjoint System ◽  
Banach Fixed Point Theorem ◽  
Structured Model ◽  
The Maximum Principle ◽  
Necessary Conditions For Optimality ◽  
Theoretical Results

This paper investigates the maximum principle for a nonlinear size-structured model that describes the optimal management of the fish resources taking into account harvesting the fish and putting the fry. We establish the well-posedness of the state system by Banach fixed-point theorem. Necessary conditions for optimality are established via the normal cone technique and adjoint system. The existence of a unique optimal policy is proved via Ekeland's variational principle and fixed-point reasoning. Finally, some examples and numerical results demonstrate the effectiveness of the theoretical results in our paper.

scholarly journals Theory of optimal harvesting for a size structured model of fish

2020 ◽  
Vol 15 ◽  
pp. 1 ◽  
Author(s):  
Rong Liu ◽  
Guirong Liu
Keyword(s):  
Necessary Optimality Conditions ◽  
Adjoint System ◽  
Optimal Harvesting ◽  
Optimal Management ◽  
Negative Solution ◽  
Structured Model ◽  
The Maximum Principle ◽  
Fish Resources ◽  
Mazur’S Theorem ◽  
Theoretical Results

This paper investigates the maximum principle for a nonlinear size structured model that describes the optimal management of the fish resources taking into account harvesting the fish and putting the fry. First, we show the existence of a unique non-negative solution of the system, and give a comparison principle. Next, we prove the existence of optimal policies by using maximizing sequence and Mazur’s theorem in convex analysis. Then, we obtain necessary optimality conditions by using tangent-normal cones and adjoint system techniques. Finally, some examples and numerical results demonstrate the effectiveness of the theoretical results in our paper.

scholarly journals Necessary Conditions for Optimality for Stochastic Evolution Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
AbdulRahman Al-Hussein
Keyword(s):  
Control Problem ◽  
Evolution Equations ◽  
Necessary Conditions ◽  
Control Variable ◽  
Evolution System ◽  
Stochastic Evolution ◽  
The Maximum Principle ◽  
Stochastic Optimal Control Problem ◽  
Necessary Conditions For Optimality ◽  
Semigroup Approach

This paper is concerned with providing the maximum principle for a control problem governed by a stochastic evolution system on a separable Hilbert space. In particular, necessary conditions for optimality for this stochastic optimal control problem are derived by using the adjoint backward stochastic evolution equation. Moreover, all coefficients appearing in this system are allowed to depend on the control variable. We achieve our results through the semigroup approach.

scholarly journals MITTAG-LEFFLER STABILITY ANALYSIS OF TEMPERED FRACTIONAL NEURAL NETWORKS WITH SHORT MEMORY AND VARIABLE-ORDER

Fractals ◽  
2021 ◽  
pp. 2140029
Author(s):  
CHUAN-YUN GU ◽  
FENG-XIA ZHENG ◽  
BABAK SHIRI
Keyword(s):  
Neural Networks ◽  
Fixed Point ◽  
Stability Analysis ◽  
Fixed Point Theorem ◽  
Banach Fixed Point Theorem ◽  
Stability Conditions ◽  
Variable Order ◽  
Numerical Examples ◽  
Short Memory ◽  
Theoretical Results

A class of tempered fractional neural networks is proposed in this paper. Stability conditions for tempered fractional neural networks are provided by using Banach fixed point theorem. Attractivity and Mittag-Leffler stability are given. In order to show the efficiency and convenience of the method used, tempered fractional neural networks with and without delay are discussed, respectively. Furthermore, short memory and variable-order tempered fractional neural networks are proposed under the global conditions. Finally, two numerical examples are used to demonstrate the theoretical results.

General necessary conditions for partially observed optimal stochastic controls

1995 ◽  
Vol 32 (4) ◽  
pp. 1118-1137 ◽  
Author(s):  
Xunjing Li ◽  
Shanjian Tang
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Control Problem ◽  
Necessary Conditions ◽  
Probabilistic Approach ◽  
The Maximum Principle ◽  
Finite Dimensional ◽  
Partially Observed ◽  
Stochastic Controls ◽  
Partially Observable

The partially observed control problem is considered for stochastic processes with control entering into the diffusion and the observation. The maximum principle is proved for the partially observable optimal control. A pure probabilistic approach is used, and the adjoint processes are characterized as solutions of related backward stochastic differential equations in finite-dimensional spaces. Most of the derivation is identified with that of the completely observable case.

General necessary conditions for partially observed optimal stochastic controls

1995 ◽  
Vol 32 (04) ◽  
pp. 1118-1137 ◽  
Author(s):  
Xunjing Li ◽  
Shanjian Tang
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Control Problem ◽  
Necessary Conditions ◽  
Probabilistic Approach ◽  
The Maximum Principle ◽  
Finite Dimensional ◽  
Partially Observed ◽  
Stochastic Controls ◽  
Partially Observable

The partially observed control problem is considered for stochastic processes with control entering into the diffusion and the observation. The maximum principle is proved for the partially observable optimal control. A pure probabilistic approach is used, and the adjoint processes are characterized as solutions of related backward stochastic differential equations in finite-dimensional spaces. Most of the derivation is identified with that of the completely observable case.

scholarly journals Controllability of conformable differential systems

2020 ◽  
Vol 25 (4) ◽  
Author(s):  
Xiaowen Wang ◽  
JinRong Wang ◽  
Michal Fečkan
Keyword(s):  
Fixed Point ◽  
Necessary Conditions ◽  
Complete Controllability ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Differential Systems ◽  
Numerical Examples ◽  
Controllability Of Systems ◽  
Sufficient And Necessary Conditions ◽  
Theoretical Results ◽  
Controllability Result

This paper deals with complete controllability of systems governed by linear and semilinear conformable differential equations. By establishing conformable Gram criterion and rank criterion, we give sufficient and necessary conditions to examine that a linear conformable system is null completely controllable. Further, we apply Krasnoselskii’s fixed point theorem to derive a completely controllability result for a semilinear conformable system. Finally, three numerical examples are given to illustrate our theoretical results.  

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