Near-Optimality in Stochastic Control of Predator-Pray System with Markov Switching

2013 ◽  
Vol 694-697 ◽  
pp. 2153-2156
Author(s):  
Xi Ning Li ◽  
Dong Mei Wei
Keyword(s):  
Optimal Control ◽  
Variational Principle ◽  
Stochastic Control ◽  
Necessary Conditions ◽  
Markov Switching ◽  
Control Variable ◽  
Ekeland’S Variational Principle ◽  
The State ◽  
Ekeland's Variational Principle ◽  
Near Optimality

In this paper, we introduce a stochastic predator-pray system with Markov switching. We establish the necessary conditions of near-optimal control for this system. The proof of the main results are based on Ito's formula, Ekeland's variational principle and some estimates on the state and the adjoint process with respect to the control variable.

Near-Optimality in Stochastic Control of Predator-Pray System with Markov Switching

2013 ◽  
Vol 319 ◽  
pp. 558-561
Author(s):  
Xi Ning Li ◽  
Dong Mei Wei
Keyword(s):  
Optimal Control ◽  
Variational Principle ◽  
Stochastic Control ◽  
Necessary Conditions ◽  
Markov Switching ◽  
Control Variable ◽  
Ekeland’S Variational Principle ◽  
The State ◽  
Ekeland's Variational Principle ◽  
Near Optimality

In this paper, we introduce a stochastic predator-pray system with Markov switching. We establish the necessary conditions of near-optimal control for this system. The proof of the main results are based on Ito's formula, Ekeland's variational principle and some estimates on the state and the adjoint process with respect to the control variable.

Near-Optimality in Stochastic Control of an Capital Accumulation System with Markovian Switching and Poisson Jumps

2013 ◽  
Vol 300-301 ◽  
pp. 627-630
Author(s):  
Ya Ting Liu ◽  
Qi Min Zhang
Keyword(s):  
Variational Principle ◽  
Stochastic Control ◽  
Capital Accumulation ◽  
Control Variable ◽  
The State ◽  
Markovian Switching ◽  
Necessary Condition ◽  
Poisson Jumps ◽  
Accumulation System ◽  
Near Optimality

We introduce a class of stochastic capital system with Marvokian switching and Poisson jumps, establish necessary condition for near-optimality. The proof of the main results is based on Ito's formula, Ekeland's variational principle and some estimates on the state and the adjoint process with respect to the control variable.

scholarly journals Ana posteriorierror analysis for an optimal control problem with point sources

2018 ◽  
Vol 52 (5) ◽  
pp. 1617-1650 ◽  
Author(s):  
Alejandro Allendes ◽  
Enrique Otárola ◽  
Richard Rankin ◽  
Abner J. Salgado
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Weighted Sobolev Spaces ◽  
Control Variable ◽  
The State ◽  
Point Sources ◽  
Adjoint Equations ◽  
Error Estimator ◽  
A Posteriori

We propose and analyze a reliable and efficienta posteriorierror estimator for a control-constrained linear-quadratic optimal control problem involving Dirac measures; the control variable corresponds to the amplitude of forces modeled as point sources. The proposeda posteriorierror estimator is defined as the sum of two contributions, which are associated with the state and adjoint equations. The estimator associated with the state equation is based on Muckenhoupt weighted Sobolev spaces, while the one associated with the adjoint is in the maximum norm and allows for unbounded right hand sides. The analysis is valid for two and three-dimensional domains. On the basis of the deviseda posteriorierror estimator, we design a simple adaptive strategy that yields optimal rates of convergence for the numerical examples that we perform.

Error Estimates of Mixed Methods for Optimal Control Problems Governed by General Elliptic Equations

2016 ◽  
Vol 8 (6) ◽  
pp. 1050-1071 ◽  
Author(s):  
Tianliang Hou ◽  
Li Li
Keyword(s):  
Optimal Control ◽  
Finite Element ◽  
Error Estimates ◽  
Elliptic Equations ◽  
Optimal Control Problems ◽  
Mixed Finite Element ◽  
Control Variable ◽  
The State ◽  
Control Problems ◽  
General Elliptic

AbstractIn this paper, we investigate the error estimates of mixed finite element methods for optimal control problems governed by general elliptic equations. The state and co-state are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control variable is approximated by piecewise constant functions. We derive L2 and H–1-error estimates both for the control variable and the state variables. Finally, a numerical example is given to demonstrate the theoretical results.

scholarly journals Remarks on Ume’s u−distance and Ekeland’s variational principle

2012 ◽  
Vol 28 (2) ◽  
pp. 257-264
Author(s):  
GEORGIANA GOGA ◽  
Keyword(s):  
Variational Principle ◽  
Ekeland’S Variational Principle ◽  
Ekeland's Variational Principle ◽  
Flower Petal ◽  
Flower Petal Theorem

The purpose of this paper is to present some remarks on Ume’s new concept of distance called u-distance, which generalizes w-distance and Suzuki’s t-distance. As an application of the u-distance version of Ekeland’s variational principle, we establish a generalized flower petal theorem.

Existence and multiplicity of solutions for discontinuous elliptic problems in ℝ N

2020 ◽  
pp. 1-25
Author(s):  
Claudianor O. Alves ◽  
Ziqing Yuan ◽  
Lihong Huang
Keyword(s):  
Variational Principle ◽  
Variational Methods ◽  
Multiple Solutions ◽  
Elliptic Problems ◽  
Ekeland’S Variational Principle ◽  
Discontinuous Nonlinearity ◽  
Nontrivial Solutions ◽  
Ekeland's Variational Principle ◽  
Multiplicity Of Solutions ◽  
Existence And Multiplicity

Abstract This paper concerns with the existence of multiple solutions for a class of elliptic problems with discontinuous nonlinearity. By using dual variational methods, properties of the Nehari manifolds and Ekeland's variational principle, we show how the ‘shape’ of the graph of the function A affects the number of nontrivial solutions.

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