共查询到20条相似文献,搜索用时 0 毫秒
1.
We study the variational inequality associated with a bounded-velocity control problem when discretionary stopping is allowed.
We establish the existence of a strong solution by using the viscosity solution techniques. The optimal policy is shown to
exist from the optimality conditions in the variational inequality. 相似文献
2.
We study the variational inequality associated with a bounded-velocity control problem when discretionary stopping is allowed.
We establish the existence of a strong solution by using the viscosity solution techniques. The optimal policy is shown to
exist from the optimality conditions in the variational inequality. 相似文献
3.
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
4.
M. Bergounioux 《Journal of Optimization Theory and Applications》1997,95(1):101-126
We investigate optimal control problems governed by variational inequalities involving constraints on the control, and more precisely the example of the obstacle problem. In this paper, we discuss some augmented Lagrangian algorithms to compute the solution. 相似文献
5.
M. Bergounioux 《Applied Mathematics and Optimization》1997,36(2):147-172
We investigate optimal control problems governed by variational inequalities, and more precisely the obstacle problem. Since
we adopt a numerical point of view, we first relax the feasible domain of the problem; then using both mathematical programming
methods and penalization methods we get optimality conditions with smooth lagrange multipliers. 相似文献
6.
《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
7.
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
8.
Shang Wei ZHU 《数学学报(英文版)》2006,22(2):607-624
In this paper, an optimal control problem for parabolic variational inequalities with delays in the highest order spatial derivatives is investigated. The well-posedness of such kinds of variational inequalities is established. The existence of optimal controls under a Cesari-type condition is proved, and the necessary conditions of Pontryagin type for optimal controls is derived. 相似文献
9.
A Simply Constrained Optimization Reformulation of KKT Systems Arising from Variational Inequalities 总被引:2,自引:0,他引:2
F. Facchinei A. Fischer C. Kanzow J. -M. Peng 《Applied Mathematics and Optimization》1999,40(1):19-37
The Karush—Kuhn—Tucker (KKT) conditions can be regarded as optimality conditions for both variational inequalities and constrained
optimization problems. In order to overcome some drawbacks of recently proposed reformulations of KKT systems, we propose
casting KKT systems as a minimization problem with nonnegativity constraints on some of the variables. We prove that, under
fairly mild assumptions, every stationary point of this constrained minimization problem is a solution of the KKT conditions.
Based on this reformulation, a new algorithm for the solution of the KKT conditions is suggested and shown to have some strong
global and local convergence properties.
Accepted 10 December 1997 相似文献
10.
We propose a method of finding the generalized solutions of nonconvex variational problems by solving an appropriate differential
inclusion that is motivated by necessary conditions of optimality for such generalized minimizers.
Accepted 28 September 1998 相似文献
11.
The paper concerns optimal control of discontinuous differential inclusions of the normal cone type governed by a generalized version of the Moreau sweeping process with control functions acting in both nonconvex moving sets and additive perturbations. This is a new class of optimal control problems in comparison with previously considered counterparts where the controlled sweeping sets are described by convex polyhedra. Besides a theoretical interest, a major motivation for our study of such challenging optimal control problems with intrinsic state constraints comes from the application to the crowd motion model in a practically adequate planar setting with nonconvex but prox-regular sweeping sets. Based on a constructive discrete approximation approach and advanced tools of first-order and second-order variational analysis and generalized differentiation, we establish the strong convergence of discrete optimal solutions and derive a complete set of necessary optimality conditions for discrete-time and continuous-time sweeping control systems that are expressed entirely via the problem data. 相似文献
12.
D. Han 《Applied Mathematics and Optimization》2002,45(1):63-74
The alternating direction method is an attractive method for solving large-scale variational inequality problems whenever
the subproblems can be solved efficiently. However, the subproblems are still variational inequality problems, which are as
structurally difficult to solve as the original one. To overcome this disadvantage, in this paper we propose a new alternating
direction method for solving a class of nonlinear monotone variational inequality problems. In each iteration the method just
makes an orthogonal projection to a simple set and some function evaluations. We report some preliminary computational results
to illustrate the efficiency of the method.
Accepted 4 May 2001. Online publication 19 October, 2001. 相似文献
13.
An optimal control problem for an elliptic obstacle variational inequality is considered. The obstacle is taken to be the
control and the solution to the obstacle problem is taken to be the state. The goal is to find the optimal obstacle from H
1
0
(Ω) so that the state is close to the desired profile while the H
1
(Ω) norm of the obstacle is not too large. Existence, uniqueness, and regularity as well as some characterizations of the optimal
pairs are established.
Accepted 11 September 1996 相似文献
14.
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
15.
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
16.
We study the Lagrange Problem of Optimal Control with a functional and control-affine dynamics
= f(t,x) + g(t,x)u and (a priori) unconstrained control u∈ \bf R
m
. We obtain conditions under which the minimizing controls of the problem are bounded—a fact which is crucial for the applicability
of many necessary optimality conditions, like, for example, the Pontryagin Maximum Principle. As a corollary we obtain conditions
for the Lipschitzian regularity of minimizers of the Basic Problem of the Calculus of Variations and of the Problem of the
Calculus of Variations with higher-order derivatives.
Accepted 15 March 1999 相似文献
17.
In this paper we develop the convergence theory of a general class of projection and contraction algorithms (PC method),
where an extended stepsize rule is used, for solving variational inequality (VI) problems. It is shown that, by defining a
scaled projection residue, the PC method forces the sequence of the residues to zero. It is also shown that, by defining a
projected function, the PC method forces the sequence of projected functions to zero. A consequence of this result is that
if the PC method converges to a nondegenerate solution of the VI problem, then after a finite number of iterations, the optimal
face is identified. Finally, we study local convergence behavior of the extragradient algorithm for solving the KKT system
of the inequality constrained VI problem. \keywords{Variational inequality, Projection and contraction method, Predictor-corrector
stepsize, Convergence property.} \amsclass{90C30, 90C33, 65K05.}
Accepted 5 September 2000. Online publication 16 January 2001. 相似文献
18.
Claudia Ceci 《Stochastics An International Journal of Probability and Stochastic Processes》2013,85(4):323-337
We consider mixed control problems for diffusion processes, i.e. problems which involve both optimal control and stopping. The running reward is assumed to be smooth, but the stopping reward need only be semicontinuous. We show that, under suitable conditions, the value function w has the same regularity as the final reward g, i.e. w is lower or upper semicontinuous if g is. Furthermore, when g is l.s.c., we prove that the value function is a viscosity solution of the associated variational inequality. 相似文献
19.
In this paper we are concerned with some optimal control problems governed by semilinear elliptic equations. The case of
a boundary control is studied. We consider pointwise constraints on the control and a finite number of equality and inequality
constraints on the state. The goal is to derive first- and second-order optimality conditions satisfied by locally optimal
solutions of the problem.
Accepted 6 May 1997 相似文献
20.
D. C. Dobson 《Applied Mathematics and Optimization》1999,40(1):61-78
The problem of designing a periodic interface between two materials in such a way that time-harmonic waves diffracted from the interface have a specified far-field pattern is studied. A minimization problem for the interface is formulated, and it is shown that solutions of constrained bounded variation exist. The differentiability of the cost functional is then studied, with no restrictions on the smoothness of the interface. Some computational issues are discussed, and finally the results of some numerical experiments are presented. Accepted 3 February 1998 相似文献