相关论文: Nonconvex penalization of switching control of par…
Optimal control problems involving hybrid binary-continuous control costs are challenging due to their lack of convexity and weak lower semicontinuity. Replacing such costs with their convex relaxation leads to a primal-dual optimality…
We consider optimal control problems for partial differential equations where the controls take binary values but vary over the time horizon, they can thus be seen as dynamic switches. The switching patterns may be subject to combinatorial…
We consider optimal control problems for partial differential equations where the controls take binary values but vary over the time horizon, they can thus be seen as dynamic switches. The switching patterns may be subject to combinatorial…
A convex penalty for promoting switching controls for partial differential equations is introduced; such controls consist of an arbitrary number of components of which at most one should be simultaneously active. Using a Moreau-Yosida…
We discuss several optimization procedures to solve finite element approximations of linear-quadratic Dirichlet optimal control problems governed by an elliptic partial differential equation posed on a 2D or 3D Lipschitz domain. The control…
This work concentrates on a class of optimal control problems for semilinear parabolic equations subject to control constraint of the form $\|u(t)\|_{L^1(\Omega)} \le \gamma$ for $t \in (0,T)$. This limits the total control that can be…
This work presents a convex-optimization-based framework for analysis and control of nonlinear partial differential equations. The approach uses a particular weak embedding of the nonlinear PDE, resulting in a linear equation in the space…
This paper considers the finite element approximation to parabolic optimal control problems with measure data in a nonconvex polygonal domain. Such problems usually possess low regularity in the state variable due to the presence of measure…
An optimal control problem for the linear wave equation with control cost chosen as the BV semi-norm in time is analyzed. This formulation enhances piecewise constant optimal controls and penalizes the number of jumps. Existence of optimal…
We consider an optimal control problem for the steady-state Kirchhoff equation, a prototype for nonlocal partial differential equations, different from fractional powers of closed operators. Existence and uniqueness of solutions of the…
We investigate the numerical approximation of an elliptic optimal control problem which involves a nonconvex local regularization of the $L^q$-quasinorm penalization (with $q\in(0,1)$) in the cost function. Our approach is based on the…
This paper focuses on stochastic optimal control problems with constraints in law, which are rewritten as optimization (minimization) of probability measures problem on the canonical space. We introduce a penalized version of this type of…
We present a method to solve a special class of parameter identification problems for an elliptic optimal control problem to global optimality. The bilevel problem is reformulated via the optimal-value function of the lower-level problem.…
We focus on finding sparse and least-$\ell_1$-norm solutions for unconstrained nonlinear optimal control problems. Such optimization problems are non-convex and non-smooth, nevertheless recent versions of Newton method for under-determined…
This paper proposes an optimal control problem for a parabolic equation with a nonlocal nonlinearity. The system is described by a parabolic equation involving a nonlinear term that depends on the solution and its integral over the domain.…
This work is concerned with a class of optimal control problems governed by a partial differential equation that are motivated by an application in radiotherapy treatment planning, where the primary design objective is to minimize the…
An optimal control problem for semilinear parabolic partial differential equations is considered. The control variable appears in the leading term of the equation. Necessary conditions for optimal controls are established by the method of…
Optimal control of the singular nonlinear parabolic PDE which is a distributional formulation of multidimensional and multiphase Stefan-type free boundary problem is analyzed. Approximating sequence of finite-dimensional optimal control…
The numerical realization of the dynamic programming principle for continuous-time optimal control leads to nonlinear Hamilton-Jacobi-Bellman equations which require the minimization of a nonlinear mapping over the set of admissible…
We consider the optimal control of singular nonlinear partial differential equation which is the distributional formulation of the multiphase Stefan type free boundary problem for the general second order parabolic equation. Boundary heat…