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1.
《Applied Mathematics and Optimization》2008,45(3):325-345
We consider the optimal control of harvesting the diffusive degenerate elliptic logistic equation. Under certain assumptions,
we prove the existence and uniqueness of an optimal control. Moreover, the optimality system and a characterization of the
optimal control are also derived. The sub-supersolution method, the singular eigenvalue problem and differentiability with
respect to the positive cone are the techniques used to obtain our results. 相似文献
2.
We consider the optimal control of harvesting the diffusive degenerate elliptic logistic equation. Under certain assumptions,
we prove the existence and uniqueness of an optimal control. Moreover, the optimality system and a characterization of the
optimal control are also derived. The sub-supersolution method, the singular eigenvalue problem and differentiability with
respect to the positive cone are the techniques used to obtain our results. 相似文献
3.
An abstract linear-quadratic regulator problem over finite time horizon is considered; it covers a large class of linear nonautonomous parabolic systems in bounded domains, with boundary control of Dirichlet or Neumann type. We give the proof of some result stated in [AT5], and in addition we prove uniqueness of the Riccati operator, provided its final datum is suitably regular. Accepted 14 October 1998 相似文献
4.
Second-Order Analysis for Control Constrained Optimal Control Problems of Semilinear Elliptic Systems 总被引:2,自引:0,他引:2
J. F. Bonnans 《Applied Mathematics and Optimization》1998,38(3):303-325
This paper presents a second-order analysis for a simple model optimal control problem of a partial differential equation,
namely, a well-posed semilinear elliptic system with constraints on the control variable only. The cost to be minimized is
a standard quadratic functional. Assuming the feasible set to be polyhedric, we state necessary and sufficient second-order
optimality conditions, including a characterization of the quadratic growth condition. Assuming that the second-order sufficient
condition holds, we give a formula for the second-order expansion of the value of the problem as well as the directional derivative
of the optimal control, when the cost function is perturbed. Then we extend the theory of second-order optimality conditions
to the case of vector-valued controls when the feasible set is defined by local and smooth convex constraints. When the space
dimension n is greater than 3, the results are based on a two norms approach, involving spaces L
2
and L
s
, with s>n/2 .
Accepted 27 January 1997 相似文献
5.
An abstract linear-quadratic regulator problem over finite time horizon is considered; it covers a large class of linear
nonautonomous parabolic systems in bounded domains, with boundary control of Dirichlet or Neumann type. The associated differential
Riccati equation is studied from the point of view of semigroup theory; it is shown to have a classical, explicitly represented
solution for very general final data; weighted H?lder regularity results for the optimal pair are deduced.
Accepted 10 December 1997 相似文献
6.
In this paper we formulate and study a minimax control problem for a class of parabolic systems with controlled Dirichlet
boundary conditions and uncertain distributed perturbations under pointwise control and state constraints. We prove an existence
theorem for minimax solutions and develop effective penalized procedures to approximate state constraints. Based on a careful
variational analysis, we establish convergence results and optimality conditions for approximating problems that allow us
to characterize suboptimal solutions to the original minimax problem with hard constraints. Then passing to the limit in approximations,
we prove necessary optimality conditions for the minimax problem considered under proper constraint qualification conditions.
Accepted 7 June 1996 相似文献
7.
Lou 《Applied Mathematics and Optimization》2008,47(2):121-142
Abstract. Optimal control problems governed by semilinear parabolic partial differential equations are considered. No Cesari-type conditions
are assumed. By proving the existence theorem and the Pontryagin maximum principle of optimal ``state-control" pairs for the
corresponding relaxed problems, an existence theorem of optimal pairs for the original problem is established. 相似文献
8.
Lou 《Applied Mathematics and Optimization》2003,47(2):121-142
Abstract. Optimal control problems governed by semilinear parabolic partial differential equations are considered. No Cesari-type conditions
are assumed. By proving the existence theorem and the Pontryagin maximum principle of optimal ``state-control" pairs for the
corresponding relaxed problems, an existence theorem of optimal pairs for the original problem is established. 相似文献
9.
Abstract. We formulate a robust optimal stopping-time problem for a state-space system and give the connection between various notions
of lower value function for the associated games (and storage function for the associated dissipative system) with solutions
of the appropriate variational inequality (VI) (the analogue of the Hamilton—Jacobi—Bellman—Isaacs equation for this setting).
We show that the stopping-time rule can be obtained by solving the VI in the viscosity sense and a positive definite supersolution
of the VI can be used for stability analysis. 相似文献
10.
Abstract. We formulate a robust optimal stopping-time problem for a state-space system and give the connection between various notions
of lower value function for the associated games (and storage function for the associated dissipative system) with solutions
of the appropriate variational inequality (VI) (the analogue of the Hamilton—Jacobi—Bellman—Isaacs equation for this setting).
We show that the stopping-time rule can be obtained by solving the VI in the viscosity sense and a positive definite supersolution
of the VI can be used for stability analysis. 相似文献
11.
12.
In this work we study the existence and asymptotic behavior of overtaking optimal trajectories for linear control systems
with convex integrands. We extend the results obtained by Artstein and Leizarowitz for tracking periodic problems with quadratic
integrands [2] and establish the existence and uniqueness of optimal trajectories on an infinite horizon. The asymptotic dynamics
of finite time optimizers is examined.
Accepted 31 January 1996 相似文献
13.
Optimal Stopping Time Formulation of Adaptive Image Filtering 总被引:1,自引:0,他引:1
This paper presents an approach to image filtering based on an optimal stopping time problem for the evolution equation describing
the filtering kernel. This approach allows us to obtain easily an adaptivity of the filter with respect to the noise level.
Well-posedness of the problem and convergence of fully discrete approximations are proved and numerical examples are presented
and discussed.
Accepted 25 October 2000. Online publication 9 April 2001. 相似文献
14.
Michael H. Freedman 《Foundations of Computational Mathematics》2001,1(2):183-204
The mathematical problem of localizing modular functors to neighborhoods of points is shown to be closely related to the
physical problem of engineering a local Hamiltonian for a computationally universal quantum medium. For genus =0 surfaces,
such a local Hamiltonian is mathematically defined. Braiding defects of this medium implements a representation associated
to the Jones polynomial and this representation is known to be universal for quantum computation.
May 15, 2000. Final version received: November 15, 2000. Online publication: February 20, 2001. 相似文献
15.
The problem of designing a periodic interface between two different materials, which gives rise to a specified far-field
diffraction pattern for a given incoming plane wave, is considered. The time harmonic waves are assumed to be TM (transverse
magnetic) polarized. The diffraction problem is modeled by a generalized Helmholtz equation with transparent boundary conditions.
In this paper the design problem is relaxed to include highly oscillatory profiles. Existence of an optimal design is established.
The principal method is based on the theory of homogenization for the model equation.
Accepted 31 May 2000. Online publication 26 February 2001. 相似文献
16.
E. N. Mahmudov 《Journal of Global Optimization》2008,41(1):31-42
Sufficient conditions for optimality are derived for partial differential inclusions of parabolic type on the basis of the
apparatus of locally conjugate mapping, and duality theorems are proved. The duality theorems proved allow one to conclude
that a sufficient condition for an extremum is an extremal relation for the direct and dual problems.
相似文献
17.
Optimality systems for optimal control problems governed by elliptic variational inequalities are derived. Existence of appropriately defined Lagrange multipliers is proved. A primal—dual active set method is proposed to solve the optimality systems numerically. Examples with and without lack of strict complementarity are included. Accepted 5 March 1999 相似文献
18.
Nabih N. Abdelmalek 《Numerical Functional Analysis & Optimization》2013,34(3-4):399-418
Two algorithms are here presented. The first one is for obtaining a Chebyshev solution of an overdetermined system of linear equations subject to bounds on the elements of the solution vector. The second algorithm is for obtaining an L1 solution of an overdetermined system of linear equations subject to the same constraints. Efficient solutions are obtained using linear programming techniques. Numerical results and comments are given. 相似文献
19.
This paper is concerned with distributed and Dirichlet boundary controls of semilinear parabolic equations, in the presence
of pointwise state constraints. The paper is divided into two parts. In the first part we define solutions of the state equation
as the limit of a sequence of solutions for equations with Robin boundary conditions. We establish Taylor expansions for solutions
of the state equation with respect to perturbations of boundary control (Theorem 5.2). For problems with no state constraints,
we prove three decoupled Pontryagin's principles, one for the distributed control, one for the boundary control, and the last
one for the control in the initial condition (Theorem 2.1). Tools and results of Part 1 are used in the second part to derive
Pontryagin's principles for problems with pointwise state constraints.
Accepted 12 July 2001. Online publication 21 December 2001. 相似文献
20.
The Bellman equation of the risk-sensitive control problem with full observation is considered. It appears as an example
of a quasi-linear parabolic equation in the whole space, and fairly general growth assumptions with respect to the space variable
x are permitted. The stochastic control problem is then solved, making use of the analytic results. The case of large deviation
with small noises is then treated, and the limit corresponds to a differential game.
Accepted 25 March 1996 相似文献