Optimal Control Problems with Mixed Control-State Constraints
نویسندگان
چکیده
Semilinear elliptic optimal control problems with pointwise control and mixed control-state constraints are considered. Necessary and sufficient optimality conditions are given. The equivalence of the SQP method and Newton’s method for a generalized equation is discussed. Local quadratic convergence of the SQP method is proved.
منابع مشابه
VARIATIONAL DISCRETIZATION AND MIXED METHODS FOR SEMILINEAR PARABOLIC OPTIMAL CONTROL PROBLEMS WITH INTEGRAL CONSTRAINT
The aim of this work is to investigate the variational discretization and mixed finite element methods for optimal control problem governed by semi linear parabolic equations with integral constraint. The state and co-state are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control is not discreted. Optimal error estimates in L2 are established for the state...
متن کاملPOD a-posteriori error analysis for optimal control problems with mixed control-state constraints
In this work linear-quadratic optimal control problems for parabolic equations with mixed control-state constraints are considered. These problems arise when a Lavrentiev regularization is utilized for state constrained linearquadratic optimal control problems. For the numerical solution a Galerkin discretization is applied utilizing proper orthogonal decomposition (POD). Based on a perturbatio...
متن کاملNonconvex Optimal Control Problems with Nonsmooth Mixed State Constraints
Necessary conditions of optimality in the form of a weak maximum principle are derived for optimal control problems with mixed constraints. Such conditions differ from previous work since they hold when a certain convexity assumption is replaced by an “interiority” assumption. Notably the result holds for problems with possibly nonsmooth mixed constraints and with additional pointwise set contr...
متن کاملA maximum principle for optimal control problems with mixed constraints
Necessary conditions in the form of maximum principles are derived for optimal control problems with mixed control and state constraints. Traditionally, necessary condtions for problems with mixed constraints have been proved under hypothesis which include the requirement that the Jacobian of the mixed constraint functional, with respect to the control variable, have full rank. We show that it ...
متن کاملSecond-order optimality conditions for a Bolza problem with mixed constraints ?
For an optimal control problem with fixed initial state and constraints on admissible controls we propose new second-order necessary optimality conditions using second-order tangents to the set of controls. In the absence of constraints on controls, our conditions are stronger than those of Gilbert and Bernstein (1983). Then, we investigate optimal control problems with fixed initial state and ...
متن کاملOptimization with the time-dependent Navier-Stokes equations as constraints
In this paper, optimal distributed control of the time-dependent Navier-Stokes equations is considered. The control problem involves the minimization of a measure of the distance between the velocity field and a given target velocity field. A mixed numerical method involving a quasi-Newton algorithm, a novel calculation of the gradients and an inhomogeneous Navier-Stokes solver, to find the opt...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- SIAM J. Control and Optimization
دوره 39 شماره
صفحات -
تاریخ انتشار 2000