PDE-Constrained Optimization Subject to Pointwise Constraints on the Control, the State, and Its Derivative

Weak-duality Based Adaptive Finite Element Methods for Pde-constrained Optimization with Pointwise Gradient State-constraints

Adaptive finite element methods for optimization problems for second order linear elliptic partial differential equations subject to pointwise constraints on the `-norm of the gradient of the state are considered. In a weak duality setting, i.e. without assuming a constraint qualification such as the existence of a Slater point, residual based a posteriori error estimators are derived. To overc...

A PDE-Constrained Generalized Nash Equilibrium Problem with Pointwise Control and State Constraints

A generalized Nash equilibrium problem (GNEP) is formulated in which, in addition to pointwise constraints on both the control and state variables, the feasible sets are partially governed by the solutions of a linear elliptic partial differential equation. The decisions (optimal controls) of the players arise in their competitors optimization problems via the righthand side of the partial diff...

Preconditioning PDE-constrained optimization with L1-sparsity and control constraints

PDE-constrained optimization aims at finding optimal setups for partial differential equations so that relevant quantities are minimized. Including sparsity promoting terms in the formulation of such problems results in more practically relevant computed controls but adds more challenges to the numerical solution of these problems. The needed L1-terms as well as additional inclusion of box cont...

extensions of some polynomial inequalities to the polar derivative

توسیع تعدادی از نامساوی های چند جمله ای در مشتق قطبی

Constrained Optimization : from LagrangianMe - hani s to Optimal Control and PDE Constraints ∗