This article is concerned with second-order necessary and sufficient optimality conditions for optimal control problems governed by 3-dimensional Navier-Stokes equations. The periodic state constraint is considered.
It is difficult to judge whether a given point is a global maximizer of an unconstrained optimization problem. This paper deals with this problem by considering global information via integral and gives a necessary an...It is difficult to judge whether a given point is a global maximizer of an unconstrained optimization problem. This paper deals with this problem by considering global information via integral and gives a necessary and sufficient condition judging whether a given point is a global maximizer of an unconstrained optimization problem. An algorithm is offered under such a condition and finally two test problems are verified via the offered algorithm.展开更多
This paper studies singular optimal control problems for systems described by nonlinear-controlled stochastic differential equations of mean-field type(MFSDEs in short),in which the coefficients depend on the state of...This paper studies singular optimal control problems for systems described by nonlinear-controlled stochastic differential equations of mean-field type(MFSDEs in short),in which the coefficients depend on the state of the solution process as well as of its expected value.Moreover,the cost functional is also of mean-field type.The control variable has two components,the first being absolutely continuous and the second singular.We establish necessary as well as sufficient conditions for optimal singular stochastic control where the system evolves according to MFSDEs.These conditions of optimality differs from the classical one in the sense that here the adjoint equation turns out to be a linear mean-field backward stochastic differential equation.The proof of our result is based on convex perturbation method of a given optimal control.The control domain is assumed to be convex.A linear quadratic stochastic optimal control problem of mean-field type is discussed as an illustrated example.展开更多
A hybridization of the three–term conjugate gradient method proposed by Zhang et al. and the nonlinear conjugate gradient method proposed by Polak and Ribi`ere, and Polyak is suggested. Based on an eigenvalue analysi...A hybridization of the three–term conjugate gradient method proposed by Zhang et al. and the nonlinear conjugate gradient method proposed by Polak and Ribi`ere, and Polyak is suggested. Based on an eigenvalue analysis, it is shown that search directions of the proposed method satisfy the sufficient descent condition, independent of the line search and the objective function convexity. Global convergence of the method is established under an Armijo–type line search condition. Numerical experiments show practical efficiency of the proposed method.展开更多
基金This work was supported by National Natural Science Foundation of China (10401041)Natural Science Foundation of Hubei Province (2004ABA009)
文摘This article is concerned with second-order necessary and sufficient optimality conditions for optimal control problems governed by 3-dimensional Navier-Stokes equations. The periodic state constraint is considered.
文摘It is difficult to judge whether a given point is a global maximizer of an unconstrained optimization problem. This paper deals with this problem by considering global information via integral and gives a necessary and sufficient condition judging whether a given point is a global maximizer of an unconstrained optimization problem. An algorithm is offered under such a condition and finally two test problems are verified via the offered algorithm.
基金The authorwould like to thank the editor,the associate editor,and anonymous referees for their constructive corrections and valuable suggestions that improved the manuscript.The author was partially supported by Algerian PNR Project Grant 08/u07/857,ATRST-(ANDRU)2011-2013.
文摘This paper studies singular optimal control problems for systems described by nonlinear-controlled stochastic differential equations of mean-field type(MFSDEs in short),in which the coefficients depend on the state of the solution process as well as of its expected value.Moreover,the cost functional is also of mean-field type.The control variable has two components,the first being absolutely continuous and the second singular.We establish necessary as well as sufficient conditions for optimal singular stochastic control where the system evolves according to MFSDEs.These conditions of optimality differs from the classical one in the sense that here the adjoint equation turns out to be a linear mean-field backward stochastic differential equation.The proof of our result is based on convex perturbation method of a given optimal control.The control domain is assumed to be convex.A linear quadratic stochastic optimal control problem of mean-field type is discussed as an illustrated example.
基金Supported by Research Council of Semnan University
文摘A hybridization of the three–term conjugate gradient method proposed by Zhang et al. and the nonlinear conjugate gradient method proposed by Polak and Ribi`ere, and Polyak is suggested. Based on an eigenvalue analysis, it is shown that search directions of the proposed method satisfy the sufficient descent condition, independent of the line search and the objective function convexity. Global convergence of the method is established under an Armijo–type line search condition. Numerical experiments show practical efficiency of the proposed method.
