相关论文: Locally Lipschitz stability of solutions to a para…

This paper is concerned with the existence and regularity of mininizers as well as of corresponding multipliers to an optimal control problem governed by semilinear elliptic equations, in which mixed pointwise control-state constraints are…

A class of optimal control problems governed by semilinear parabolic equations with mixed pointwise constraints is considered. We give some criteria under which the first and second-order optimality conditions are of KKT-type. We then prove…

The paper investigates stability properties of solutions of optimal control problems for semilinear parabolic partial differential equations. H\"older or Lipschitz dependence of the optimal solution on perturbations are obtained for…

In this paper we apply an augmented Lagrange method to a class of semilinear elliptic optimal control problems with pointwise state constraints. We show strong convergence of subsequences of the primal variables to a local solution of the…

The local stability of the solution map to a parametric boundary control problem governed by semilinear elliptic equations with finite mixed pointwise constraints is considered in this paper. We prove that the solution map is locally…

We study a control problem governed by a semilinear parabolic equation with pointwise control and state constraints imposed at every point of the space-time cylinder. We obtain second order sufficient optimality conditions for local…

The paper presents results about strong metric subregularity of the optimality mapping associated with the system of first-order necessary optimality conditions for a problem of optimal control of a semilinear parabolic equation. The…

A class of time-optimal control problems governed by semilinear parabolic equations with mixed pointwise constraints and final point constraints is considered. By introducing the so-called locally optimal solution to time-optimal control…

We study the optimal value function for control problems on Banach spaces that involve both continuous and discrete control decisions. For problems involving semilinear dynamics subject to mixed control inequality constraints, one can show…

This paper is concerned with first- and second-order optimality conditions as well as the stability for non-smooth semilinear optimal control problems involving the $L^1$-norm of the control in the cost functional. In addition to the…

This paper studies stability aspects of solutions of parametric mathematical programs and generalized equations, respectively, with disjunctive constraints. We present sufficient conditions that, under some constraint qualifications…

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…

We consider the Lagrange problem of optimal control with unrestricted controls and address the question: under what conditions we can assure optimal controls are bounded? This question is related to the one of Lipschitzian regularity of…

Degenerate abstract parabolic equations with variable coefficients are studied. Here the boundary conditions are nonlocal. The maximal regularity properties of solutions for elliptic and parabolic problems and Strichartz type estimates in…

We would like to study the solution stability of a parametric control problem governed by semilinear elliptic equations with a mixed state-control constraint, where the cost function is nonconvex and the admissible set is unbounded. The…

We discuss first order optimality conditions for geometric optimization problems with Neumann boundary conditions and boundary observation. The methods we develop here are applicable to large classes of state systems or cost functionals.…

This paper is dedicated to the stability analysis of the optimal solutions of a control problem associated with a semilinear elliptic equation. The linear differential operator of the equation is neither monotone nor coercive due to the…

In this work, we shall study the nonlinear inverse problems of recovering the Robin coefficients in elliptic and parabolic systems of second order, and establish their local Lipschitz stabilities. Some local Lipschitz stability was derived…

A class of optimal control problems governed by semilinear parabolic equations with mixed constraints and a box constraint for control variable is considered. We show that if the separation condition is satisfied, then both optimality…

Much is known about when a locally optimal solution depends in a single-valued Lipschitz continuous way on the problem's parameters, including tilt perturbations. Much less is known, however, about when that solution and a uniquely…