The Experts below are selected from a list of 8832 Experts worldwide ranked by ideXlab platform
Yu. N. Kiselev - One of the best experts on this subject based on the ideXlab platform.
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optimal processes in the model of two sector economy with an integral utility function
Differential Equations, 2017Co-Authors: Yu. N. Kiselev, Michael V. Orlov, S M OrlovAbstract:An infinite-horizon two-sector economy model with a Cobb–Douglas production function is studied for different depreciation rates, the utility function being an integral functional with discounting and a logarithmic integrand. The application of the Pontryagin maximum principle leads to a boundary value problem with special conditions at infinity. The presence of singular modes in the optimal Solution complicates the search for a Solution to the boundary value problem of the maximum principle. To construct the Solution to the boundary value problem, the singular modes are written in an analytical form; in addition, a special version of the sweep algorithm in continuous form is proposed. The optimality of the Extremal Solution is proved.
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boundary value problem of pontryagin s maximum principle in a two sector economy model with an integral utility function
Computational Mathematics and Mathematical Physics, 2015Co-Authors: Yu. N. Kiselev, M V Orlov, S M OrlovAbstract:An infinite-horizon two-sector economy model with a Cobb–Douglas production function and a utility function that is an integral functional with discounting and a logarithmic integrand is investigated. The application of Pontryagin’s maximum principle yields a boundary value problem with special conditions at infinity. The search for the Solution of the maximum-principle boundary value problem is complicated by singular modes in its optimal Solution. In the construction of the Solution to the problem, they are described in analytical form. Additionally, a special version of the sweep method in continuous form is proposed, which is of interest from theoretical and computational points of view. An important result is the proof of the optimality of the Extremal Solution obtained by applying the maximum-principle boundary value problem.
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Boundary value problem of Pontryagin’s maximum principle in a two-sector economy model with an integral utility function
Computational Mathematics and Mathematical Physics, 2015Co-Authors: Yu. N. Kiselev, M V Orlov, S M OrlovAbstract:An infinite-horizon two-sector economy model with a Cobb–Douglas production function and a utility function that is an integral functional with discounting and a logarithmic integrand is investigated. The application of Pontryagin’s maximum principle yields a boundary value problem with special conditions at infinity. The search for the Solution of the maximum-principle boundary value problem is complicated by singular modes in its optimal Solution. In the construction of the Solution to the problem, they are described in analytical form. Additionally, a special version of the sweep method in continuous form is proposed, which is of interest from theoretical and computational points of view. An important result is the proof of the optimality of the Extremal Solution obtained by applying the maximum-principle boundary value problem.
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optimal resource allocation program in a two sector economic model with an integral type functional for various amortization factors
Differential Equations, 2015Co-Authors: Yu. N. Kiselev, Michael V. Orlov, S M OrlovAbstract:We study the resource allocation problem in a two-sector economic model with a two-factor Cobb–Douglas production function for various amortization factors on a finite time horizon with a functional of the integral type. The problem is reduced to a canonical form by scaling the state variables and time. We show that the Extremal Solution constructed with the use of the maximum principle is optimal. For a sufficiently large planning horizon, the optimal control has two or three switching points, contains one singular segment, and is zero on the terminal part. The considered problem with different production functions admits a biological interpretation in a model of balanced growth of plants on a given finite time interval.
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Optimal resource distribution program in a two-sector economic model with a Cobb-Douglas production function with distinct amortization factors
Differential Equations, 2012Co-Authors: Yu. N. Kiselev, Michael V. OrlovAbstract:We consider a resource distribution problem on a finite time interval with a terminal functional for a two-sector economic model with a two-factor Cobb-Douglas production function with distinct amortization factors. The problem can be reduced to a canonical form by scaling the state variables and time. We prove the optimality of an Extremal Solution constructed with the use of the maximum principle. For the case in which the initial state of the plant lies above the singular ray, the Solution of the boundary value problem of the maximum principle is presented in closed form.
Guangren Duan - One of the best experts on this subject based on the ideXlab platform.
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a neighboring Extremal Solution for an optimal switched impulsive control problem
Journal of Industrial and Management Optimization, 2012Co-Authors: Canghua Jiang, K L Teo, Ryan Loxton, Guangren DuanAbstract:This paper presents a neighboring Extremal Solution for a class of optimal switched impulsive control problems with perturbations in the initial state, terminal condition and system's parameters. The sequence of mode's switching is pre-specified, and the decision variables, i.e. the switching times and parameters of the system involved, have inequality constraints. It is assumed that the active status of these constraints is unchanged with the perturbations. We derive this Solution by expanding the necessary conditions for optimality to first-order and then solving the resulting multiple-point boundary-value problem by the backward sweep technique. Numerical simulations are presented to illustrate this Solution method.
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a neighboring Extremal Solution for optimal switched impulsive control problems with large perturbations
International Journal of Innovative Computing Information and Control, 2012Co-Authors: Canghua Jiang, K L Teo, Ryan Loxton, Guangren DuanAbstract:This paper presents an approach to compute the neighboring Extremal solu- tion for an optimal switched impulsive control problem with a pre-specied sequence of modes and a large perturbation in the initial state. The decision variables { the subsys- tem switching times and the control parameters { are subject to inequality constraints. Since the active status of these inequality constraints may change under the large pertur- bation, we add fractions of the initial perturbation separately such that the active status of the inequality constraints is invariant during each step, and compute the neighboring Extremal Solution iteratively by solving a sequence of quadratic programming problems. First, we compute a correction direction for the control in the perturbed system through an extended backward sweep technique. Then, we compute the maximal step size in this direction and derive the Solution iteratively by using a revised active set strategy. An example problem involving a shrimp harvesting operation demonstrates that our Solution approach is faster than the sequential quadratic programming approach.
Manel Sanchón - One of the best experts on this subject based on the ideXlab platform.
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W1,q estimates for the Extremal Solution of reaction-diffusion problems
Nonlinear Analysis: Theory Methods & Applications, 2013Co-Authors: Manel SanchónAbstract:Abstract We establish a new W 1 , 2 n − 1 n − 2 estimate for the Extremal Solution of − Δ u = λ f ( u ) in a smooth bounded domain Ω of R n , which is convex, for arbitrary positive and increasing nonlinearities f ∈ C 1 ( R ) satisfying lim t → + ∞ f ( t ) / t = + ∞ .
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$W^{1,q}$ estimates for the Extremal Solution of reaction-diffusion problems
arXiv: Analysis of PDEs, 2012Co-Authors: Manel SanchónAbstract:We establish a new $W^{1,2\frac{n-1}{n-2}}$ estimate for the Extremal Solution of $-\Delta u=\lambda f(u)$ in a smooth bounded domain $\Omega$ of $\mathbb{R}^n$, which is convex, for arbitrary positive and increasing nonlinearities $f\in C^1(\mathbb{R})$ satisfying $\lim_{t\rightarrow +\infty}f(t)/t=+\infty$.
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w 1 q estimates for the Extremal Solution of reaction diffusion problems
arXiv: Analysis of PDEs, 2012Co-Authors: Manel SanchónAbstract:We establish a new $W^{1,2\frac{n-1}{n-2}}$ estimate for the Extremal Solution of $-\Delta u=\lambda f(u)$ in a smooth bounded domain $\Omega$ of $\mathbb{R}^n$, which is convex, for arbitrary positive and increasing nonlinearities $f\in C^1(\mathbb{R})$ satisfying $\lim_{t\rightarrow +\infty}f(t)/t=+\infty$.
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Regularity of radial minimizers of reaction equations involving the p-Laplacian
arXiv: Analysis of PDEs, 2007Co-Authors: Xavier Cabré, Antonio Capella, Manel SanchónAbstract:We consider semi-stable, radially symmetric, and decreasing Solutions of a reaction equation involving the p-Laplacian, where the reaction term is a locally Lipschitz function, and the domain is the unit ball. For this class of radial Solutions, which includes local minimizers, we establish pointwise and Sobolev estimates which are optimal and do not depend on the specific nonlinear reaction term. Under standard assumptions we also prove the regularity of the corresponding Extremal Solution.
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Regularity of the Extremal Solution of Some Nonlinear Elliptic Problems Involving the p-Laplacian
Potential Analysis, 2007Co-Authors: Manel SanchónAbstract:We consider the equation $ - {\text{div}}{\left( {{\left| {\nabla u} \right|}^{{p - 2}} \nabla u} \right)} = \lambda f{\left( u \right)}$ on a smooth bounded domain of $\mathbb{R}^{N} $ with zero Dirichlet boundary conditions where p ≥ 2, λ > 0 and f satisfies typical assumptions in the subject of Extremal Solutions. We prove that, for such general nonlinearities f , the Extremal Solution u ^* belongs to L ^ ∞ (Ω) if N
Michael V. Orlov - One of the best experts on this subject based on the ideXlab platform.
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optimal processes in the model of two sector economy with an integral utility function
Differential Equations, 2017Co-Authors: Yu. N. Kiselev, Michael V. Orlov, S M OrlovAbstract:An infinite-horizon two-sector economy model with a Cobb–Douglas production function is studied for different depreciation rates, the utility function being an integral functional with discounting and a logarithmic integrand. The application of the Pontryagin maximum principle leads to a boundary value problem with special conditions at infinity. The presence of singular modes in the optimal Solution complicates the search for a Solution to the boundary value problem of the maximum principle. To construct the Solution to the boundary value problem, the singular modes are written in an analytical form; in addition, a special version of the sweep algorithm in continuous form is proposed. The optimality of the Extremal Solution is proved.
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optimal resource allocation program in a two sector economic model with an integral type functional for various amortization factors
Differential Equations, 2015Co-Authors: Yu. N. Kiselev, Michael V. Orlov, S M OrlovAbstract:We study the resource allocation problem in a two-sector economic model with a two-factor Cobb–Douglas production function for various amortization factors on a finite time horizon with a functional of the integral type. The problem is reduced to a canonical form by scaling the state variables and time. We show that the Extremal Solution constructed with the use of the maximum principle is optimal. For a sufficiently large planning horizon, the optimal control has two or three switching points, contains one singular segment, and is zero on the terminal part. The considered problem with different production functions admits a biological interpretation in a model of balanced growth of plants on a given finite time interval.
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Optimal resource distribution program in a two-sector economic model with a Cobb-Douglas production function with distinct amortization factors
Differential Equations, 2012Co-Authors: Yu. N. Kiselev, Michael V. OrlovAbstract:We consider a resource distribution problem on a finite time interval with a terminal functional for a two-sector economic model with a two-factor Cobb-Douglas production function with distinct amortization factors. The problem can be reduced to a canonical form by scaling the state variables and time. We prove the optimality of an Extremal Solution constructed with the use of the maximum principle. For the case in which the initial state of the plant lies above the singular ray, the Solution of the boundary value problem of the maximum principle is presented in closed form.
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Optimum control laws in a non-autonomous dynamic model of a gas field
Moscow University Computational Mathematics and Cybernetics, 2011Co-Authors: Yu. N. Kiselev, Michael V. OrlovAbstract:A model of gas field development described as a nonlinear optimum control problem with an infinite planning horizon is considered. The Pontryagin maximum principle is used to solve it. The theorem on sufficient optimumity conditions in terms of constructions of the Pontryagin maximum principles is used to substantiate the optimumity of the Extremal Solution. A procedure for constructing the optimum Solution by dynamic programming is described and is of some methodological interest. The obtained optimum Solution is used to construct the Bellman function. Reference is made to a work containing an economic interpretation of the problem.
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Analysis of a Gas Field Development Model with an Infinite Planning Horizon
Differential Equations, 2011Co-Authors: Yu. N. Kiselev, Michael V. OrlovAbstract:We consider a nonlinear optimal control problem with an infinite planning horizon, which extends a dynamic gas field development model by taking into account a gas price forecast. (The prices varies in time.) The Solution is constructed on the basis of the Pontryagin maximum principle. To prove the optimality of the Extremal Solution, we use the theorem on sufficient optimality conditions in terms of constructions of the Pontryaginmaximum principle. We discuss the problem of constructing an optimal Solution by dynamic programming.
S M Orlov - One of the best experts on this subject based on the ideXlab platform.
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optimal processes in the model of two sector economy with an integral utility function
Differential Equations, 2017Co-Authors: Yu. N. Kiselev, Michael V. Orlov, S M OrlovAbstract:An infinite-horizon two-sector economy model with a Cobb–Douglas production function is studied for different depreciation rates, the utility function being an integral functional with discounting and a logarithmic integrand. The application of the Pontryagin maximum principle leads to a boundary value problem with special conditions at infinity. The presence of singular modes in the optimal Solution complicates the search for a Solution to the boundary value problem of the maximum principle. To construct the Solution to the boundary value problem, the singular modes are written in an analytical form; in addition, a special version of the sweep algorithm in continuous form is proposed. The optimality of the Extremal Solution is proved.
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boundary value problem of pontryagin s maximum principle in a two sector economy model with an integral utility function
Computational Mathematics and Mathematical Physics, 2015Co-Authors: Yu. N. Kiselev, M V Orlov, S M OrlovAbstract:An infinite-horizon two-sector economy model with a Cobb–Douglas production function and a utility function that is an integral functional with discounting and a logarithmic integrand is investigated. The application of Pontryagin’s maximum principle yields a boundary value problem with special conditions at infinity. The search for the Solution of the maximum-principle boundary value problem is complicated by singular modes in its optimal Solution. In the construction of the Solution to the problem, they are described in analytical form. Additionally, a special version of the sweep method in continuous form is proposed, which is of interest from theoretical and computational points of view. An important result is the proof of the optimality of the Extremal Solution obtained by applying the maximum-principle boundary value problem.
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Boundary value problem of Pontryagin’s maximum principle in a two-sector economy model with an integral utility function
Computational Mathematics and Mathematical Physics, 2015Co-Authors: Yu. N. Kiselev, M V Orlov, S M OrlovAbstract:An infinite-horizon two-sector economy model with a Cobb–Douglas production function and a utility function that is an integral functional with discounting and a logarithmic integrand is investigated. The application of Pontryagin’s maximum principle yields a boundary value problem with special conditions at infinity. The search for the Solution of the maximum-principle boundary value problem is complicated by singular modes in its optimal Solution. In the construction of the Solution to the problem, they are described in analytical form. Additionally, a special version of the sweep method in continuous form is proposed, which is of interest from theoretical and computational points of view. An important result is the proof of the optimality of the Extremal Solution obtained by applying the maximum-principle boundary value problem.
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optimal resource allocation program in a two sector economic model with an integral type functional for various amortization factors
Differential Equations, 2015Co-Authors: Yu. N. Kiselev, Michael V. Orlov, S M OrlovAbstract:We study the resource allocation problem in a two-sector economic model with a two-factor Cobb–Douglas production function for various amortization factors on a finite time horizon with a functional of the integral type. The problem is reduced to a canonical form by scaling the state variables and time. We show that the Extremal Solution constructed with the use of the maximum principle is optimal. For a sufficiently large planning horizon, the optimal control has two or three switching points, contains one singular segment, and is zero on the terminal part. The considered problem with different production functions admits a biological interpretation in a model of balanced growth of plants on a given finite time interval.
