共查询到20条相似文献,搜索用时 15 毫秒
1.
Jukka Lempa 《Mathematical Methods of Operations Research》2008,67(2):257-268
The objective of this study is to provide an alternative characterization of the optimal value function of a certain Black–Scholes-type
optimal stopping problem where the underlying stochastic process is a general random walk, i.e. the process constituted by
partial sums of an IID sequence of random variables. Furthermore, the pasting principle of this optimal stopping problem is
studied.
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2.
This note discusses the existence of the directional derivatives of the optimal value functions in a class of nonlinear programming problems and gives the expressions of the directional derivatives. In the study, it is not assumed that the optimal set at the point discussed is not empty. Many well-known results of this area can be derived as special cases of the main theorems of this note.This research was supported by the National Science Foundation of China. The authors would like to thank Professor A. V. Fiacco and the referees for their helpful suggestions. 相似文献
3.
Impulsive optimal control with finite or infinite time horizon 总被引:1,自引:0,他引:1
A. Blaquière 《Journal of Optimization Theory and Applications》1985,46(4):431-439
We consider a dynamical system subjected to feedback optimal control in such a way that the evolution of the state exhibits both sudden jumps and continuous changes. Previously obtained necessary conditions (Ref. 1) for such impulsive optimal feedback controls are generalized to admit the case of infinite time horizon; this generalization permits application to a wider class of problems. The results are illustrated by application to a version of the innkeeper's problem.Dedicated to G. Leitmann 相似文献
4.
On the class of infinite horizon optimal control problems affine,which are structurally stable 下载免费PDF全文
M'hamed Kesri 《Mathematical Methods in the Applied Sciences》2016,39(11):2799-2807
We prove in this article that there is in the set of all problems we consider a subset, which is residual. Every problem in this subset is shown to be structurally stable and defines a dynamical system, which looks like the graph of the figure given in Section 1 , contrary to what happens for ordinary dynamical systems, that is, the ones associated with ODEs. There, the initial value problem (in the smooth case) is uniquely solvable; the structurally stable systems look like the figure given in Section 1 , but sources are equilibria. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
5.
A method for solving optimal control problems with general elliptic operators is presented and analyzed. Especially, estimates
of the rate of convergence for the control problems with the proposed approach are derived independently of the underlying
approximation method. Some numerical experiments with the proposed method are included. 相似文献
6.
The aim of this paper is to provide an alternate treatment of the homogenization of an optimal control problem in the framework
of two-scale (multi-scale) convergence in the periodic case. The main advantage of this method is that we are able to show
the convergence of cost functionals directly without going through the adjoint equation. We use a corrector result for the
solution of the state equation to achieve this. 相似文献
7.
Connections between the covector mapping theorem and convergence of pseudospectral methods for optimal control 总被引:2,自引:0,他引:2
Qi Gong I. Michael Ross Wei Kang Fariba Fahroo 《Computational Optimization and Applications》2008,41(3):307-335
In recent years, many practical nonlinear optimal control problems have been solved by pseudospectral (PS) methods. In particular,
the Legendre PS method offers a Covector Mapping Theorem that blurs the distinction between traditional direct and indirect
methods for optimal control. In an effort to better understand the PS approach for solving control problems, we present consistency
results for nonlinear optimal control problems with mixed state and control constraints. A set of sufficient conditions is
proved under which a solution of the discretized optimal control problem converges to the continuous solution. Convergence
of the primal variables does not necessarily imply the convergence of the duals. This leads to a clarification of the Covector
Mapping Theorem in its relationship to the convergence properties of PS methods and its connections to constraint qualifications.
Conditions for the convergence of the duals are described and illustrated. An application of the ideas to the optimal attitude
control of NPSAT1, a highly nonlinear spacecraft, shows that the method performs well for real-world problems.
The research was supported in part by NPS, the Secretary of the Air Force, and AFOSR under grant number, F1ATA0-60-6-2G002. 相似文献
8.
We consider optimal control problems of infinite horizon type, whose control laws are given by L1loc‐functions and whose objective function has the meaning of a discounted utility. Our main objective is the verification of the fact that the value function is a viscosity solution of the Hamilton‐Jacobi‐Bellman (HJB) equation in this framework. The usual final condition for the HJB‐equation in the finite horizon case (V (T, x) = 0 or V (T, x) = g(x)) has to be substituted by a decay condition at the infinity. Following the dynamic programming approach, we obtain Bellman's optimality principle and the dynamic programming equation (see (3)). We also prove a regularity result (local Lipschitz continuity) for the value function. 相似文献
9.
In recent years,a nonoverlapping domain decomposition iterative procedure,which is based on using Robin-type boundary conditions as information transmission conditions on the subdomain interfaces,has been developed and analyzed.It is known that the convergence rate of this method is 1-O(h),where h is mesh size.In this paper,the convergence rate is improved to be 1-O(h1/2 H-1/2)sometime by choosing suitable parameter,where H is the subdomain size.Counter examples are constructed to show that our convergence estimates are sharp,which means that the convergence rate cannot be better than 1-O(h1/2H-1/2)in a certain case no matter how parameter is chosen. 相似文献
10.
We analyze the rate of local convergence of the augmented Lagrangian method in nonlinear semidefinite optimization. The presence
of the positive semidefinite cone constraint requires extensive tools such as the singular value decomposition of matrices,
an implicit function theorem for semismooth functions, and variational analysis on the projection operator in the symmetric
matrix space. Without requiring strict complementarity, we prove that, under the constraint nondegeneracy condition and the
strong second order sufficient condition, the rate of convergence is linear and the ratio constant is proportional to 1/c, where c is the penalty parameter that exceeds a threshold .
The research of Defeng Sun is partly supported by the Academic Research Fund from the National University of Singapore. The
research of Jie Sun and Liwei Zhang is partly supported by Singapore–MIT Alliance and by Grants RP314000-042/057-112 of the
National University of Singapore. The research of Liwei Zhang is also supported by the National Natural Science Foundation
of China under project grant no. 10471015 and by the Scientific Research Foundation for the Returned Overseas Chinese Scholars,
State Education Ministry, China. 相似文献
11.
G. Sorger 《Journal of Optimization Theory and Applications》1992,72(1):143-162
This paper presents local optimality and stability conditions for stationary solutions of autonomous optimal control problems with a positive rate of discounting. The conditions do not require the Hamiltonian function to be concave with respect to the state variables. Two examples from optimal economic growth theory are discussed to show that our results can be applied in situations when other known stability conditions fail to be satisfied.Part of this paper was written while the author visited the Faculty of Management at the University of Toronto. Support from SSHRC Grant 410-83-9888 and from Grant P6601 of the Austrian Science Foundation is gratefully acknowledged. 相似文献
12.
By using the definition of Γ-convergence for vector valued functions given in Oppezzi and Rossi (Optimization, to appear),
we obtain a property of infimum values of the Γ-limit. By generalizing Mosco convergence to vector valued functions, we also
obtain, in the convex case, the extension of some stability results analogous to the ones in Oppezzi and Rossi (optimization,
to appear), when domain and value space are infinite dimensional.
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13.
14.
A. Cellina F. Monti M. Spadoni 《Nonlinear Analysis: Theory, Methods & Applications》2008,69(7):1966-1970
We consider a time optimal problem for a system described by a differential inclusion, whose right hand side is not necessarily convex valued. Under the assumption of strict convexity of the map obtained by convexifying the original, non-convex valued map, we obtain the strong convergence of the derivatives of any uniformly converging minimizing sequence. The assumptions required by this result are satisfied, for instance, by the classical brachystochrone problem and by Fermat’s principle. 相似文献
15.
16.
Lisa A. Korf 《Annals of Operations Research》2006,142(1):165-186
Traditional approaches to solving stochastic optimal control problems involve dynamic programming, and solving certain optimality
equations. When recast as stochastic programming problems, structural aspects such as convexity are retained, and numerical
solution procedures based on decomposition and duality may be exploited. This paper explores a class of stationary, infinite-horizon
stochastic optimization problems with discounted cost criterion. Constraints on both states and controls are permitted, and
modeled in the objective function by allowing it to take infinite values. Approximating techniques are developed using variational
analysis, and intuitive lower bounds are obtained via averaging the future. These bounds could be used in a finite-time horizon
stochastic programming setting to find solutions numerically.
Research supported in part by a grant of the National Science Foundation.
AMS Classification 46N10, 49N15, 65K10, 90C15, 90C46 相似文献
17.
Summary A generalized linear rank statistic is introduced to include, as special cases, both signed as well as unsigned linear rank
statistics. For this statistic, the rate of convergence to asymptotic normality is investigated. It is shown that this rate
is of orderO(N
−1/2 logN) if the score generating function ϕ is twice differentiable, and it is of orderO(N
−1/2) if the second derivative of ϕ satisfies Lipschitz's condition of order ≧1/2. The results obtained extend as well as generalize
most of the earlier results obtained in this direction. 相似文献
18.
A. S. Tikhomirov 《Computational Mathematics and Mathematical Physics》2007,47(5):780-790
An estimate of the convergence rate of some homogeneous Markov monotone random search optimization algorithms is obtained. 相似文献
19.
We study the projected gradient algorithm for linearly constrained optimization. Wolfe (Ref. 1) has produced a counterexample to show that this algorithm can jam. However, his counterexample is only 1(
n
), and it is conjectured that the algorithm is convergent for 2-functions. We show that this conjecture is partly right. We also show that one needs more assumptions to prove convergence, since we present a family of counterexamples. We finally give a demonstration that no jamming can occur for quadratic objective functions.This work was supported by the Natural Sciences and Engineering Research Council of Canada 相似文献
20.
Ben Adcock 《Journal of Approximation Theory》2011,163(11):1638-1674
We consider expansions of smooth, nonperiodic functions defined on compact intervals in eigenfunctions of polyharmonic operators equipped with homogeneous Neumann boundary conditions. Having determined asymptotic expressions for both the eigenvalues and eigenfunctions of these operators, we demonstrate how these results can be used in the efficient computation of expansions. Next, we consider the convergence. We establish the key advantage of such expansions over classical Fourier series–namely, both faster and higher-order convergence–and provide a full asymptotic expansion for the error incurred by the truncated expansion. Finally, we derive conditions that completely determine the convergence rate. 相似文献