The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
The study of small magnetic particles has become a very important topic, in particular for the development of technological devices such as those used for magnetic recording. In this field, switching the magnetization inside the magnetic sample is of particular relevance. We here investigate mathematically this problem by considering the full partial differential model of Landau-Lifschitz equations triggered by a uniform (in space) external magnetic field.
The study of small magnetic particles has become a very important topic, in
particular for the development of technological devices such as those
used for magnetic recording. In this field, switching the magnetization inside
the magnetic sample is of particular relevance. We here investigate mathematically
this problem by considering the full partial differential model of Landau-Lifschitz
equations triggered by a uniform (in space) external magnetic field.
We consider a financial market with memory effects in which wealth processes are driven by mean-field stochastic Volterra equations. In this financial market, the classical dynamic programming method can not be used to study the optimal investment problem, because the solution of mean-field stochastic Volterra equation is not a Markov process. In this paper, a new method through Malliavin calculus introduced in [1], can be used to obtain the optimal investment in a Volterra type financial market....
The maximum principle for optimal control problems of fully coupled forward-backward doubly stochastic differential equations (FBDSDEs in short) in the global form is obtained, under the assumptions that the diffusion coefficients do not contain the control variable, but the control domain need not to be convex. We apply our stochastic maximum principle (SMP in short) to investigate the optimal control problems of a class of stochastic partial differential equations (SPDEs in short). And as an example...
The maximum principle for optimal control problems of fully coupled
forward-backward doubly stochastic differential equations (FBDSDEs in short)
in the global form is obtained, under the assumptions that the diffusion
coefficients do not contain the control variable, but the control domain
need not to be convex. We apply our stochastic maximum principle (SMP in
short) to investigate the optimal control problems of a class of stochastic
partial differential equations (SPDEs in short). And as an...
This paper deals with the optimal control problem in which the controlled system is described by a fully coupled anticipated forward-backward stochastic differential delayed equation. The maximum principle for this problem is obtained under the assumption that the diffusion coefficient does not contain the control variables and the control domain is not necessarily convex. Both the necessary and sufficient conditions of optimality are proved. As illustrating examples, two kinds of linear quadratic...
Optimal control problems for the heat equation with pointwise bilateral control-state constraints are considered. A locally superlinearly convergent numerical solution algorithm is proposed and its mesh independence is established. Further, for the efficient numerical solution reduced space and Schur complement based preconditioners are proposed which take into account the active and inactive set structure of the problem. The paper ends by numerical tests illustrating our theoretical findings and...
Optimal control problems for the heat equation with pointwise
bilateral control-state constraints are considered. A locally
superlinearly convergent numerical solution algorithm is proposed
and its mesh independence is established. Further, for the
efficient numerical solution reduced space and Schur complement
based preconditioners are proposed which take into account the
active and inactive set structure of the problem. The paper ends
by numerical tests illustrating our theoretical findings and
comparing...
This paper is devoted to describing second order conditions in the framework of extremal problems, that is, conditions obtained by reducing the optimal control problem to an abstract one in a suitable Banach (or Hilbert) space. The studied problem includes equality constraints both on the end-points and on the state-control trajectory. The second goal is to give a complete description of necessary and sufficient second order conditions for weak local optimality by describing first the associated...
In this work, the least pointwise upper and/or lower bounds on the state variable on a specified subdomain of a control system under piecewise constant control action are sought. This results in a non-smooth optimization problem in function spaces. Introducing a Moreau-Yosida regularization of the state constraints, the problem can be solved using a superlinearly convergent semi-smooth Newton method. Optimality conditions are derived, convergence of the Moreau-Yosida regularization is proved, and...
In this work, the least pointwise upper and/or lower bounds on the state variable
on a specified subdomain of a control system under piecewise constant control action are sought.
This results in a non-smooth optimization problem in function spaces. Introducing a Moreau-Yosida
regularization of the state constraints, the problem can be solved
using a superlinearly convergent semi-smooth Newton method.
Optimality conditions are derived, convergence of the Moreau-Yosida
regularization is proved, and...
In this paper we study the minimax control of systems governed by a nonlinear evolution inclusion of the subdifferential type. Using some continuity and lower semicontinuity results for the solution map and the cost functional respectively, we are able to establish the existence of an optimal control. The abstract results are then applied to obstacle problems, semilinear systems with weakly varying coefficients (e.gȯscillating coefficients) and differential variational inequalities.
Currently displaying 1 –
20 of
31