This paper addresses complementarity problems motivated by constrained optimal control problems. It is shown that the primal-dual active set strategy, which is known to be extremely efficient for this class of problems, and a specific semismooth Newton method lead to identical algorithms. The notion of slant differentiability is recalled and it is argued that the max-function is slantly differentiable in L p-spaces when appropriately combined with a two-norm concept. This leads to new local convergence results of the primal-dual active set strategy. Global unconditional convergence results are obtained by means of appropriate merit functions.

No abstract

No abstract

An algorithm for efficient solution of control constrained optimal control problems is proposed and analyzed. It is based on an active set strategy involving primal as well as dual variables. For discretized problems sufficient conditions for convergence in finitely many iterations are given. Numerical examples are given and the role of strict complementarity condition is discussed.

This article presents a reduced-order modeling approach for simulation and control of viscous incompressible flows. The reduced-order models suitable for control and which capture the essential physics are developed using the reduced-basis method. The so-called Lagrange approach is used to define reduced bases and the basis functions in this approach are obtained from the numerical solutions. The feasibility of this method for flow control is demonstrated on boundary control problems in closed cavity and in wall-bounded channel flows. Control action is effected through boundary surface movement on a part of the solid wall. Our formulation of the reduced-order method applied to flow control problems leads to a constrained minimization problem and is solved by applying Newton-like methods to the necessary conditions of optimality. Through our computational experiments we demonstrate the feasibility and applicability of the reduced-order method for simulation and control of fluid flows. c 1998 Academic PressKey Words: reduced-basis method; reduced-order modeling; Navier-Stokes equations; finite element; optimal control.