Optimization problems with partial differential equation (PDE) constraints arise in many science and engineering applications. Their robust and efficient solution present many mathematical challenges and requires a tight integration of properties and structures of the underlying problem, of fast numerical PDE solvers, and of numerical nonlinear optimization. This workshop brought together exper...

Sundance is a package in the Trilinos suite designed to provide high-level components for the development of highperformance PDE simulators with built-in capabilities for PDE-constrained optimization. We review the implications of PDE-constrained optimization on simulator design requirements, then survey the architecture of the Sundance problem specification components. These components allow i...

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...

A method for simultaneously constructing a reduced-order model and using it as a surrogate model to solve a PDE-constrained optimization problem is introduced. A reducedorder model is built for the parameters corresponding to the initial guess of the optimization problem. Since the resulting reduced-order model can be expected to be accurate only in the vicinity of this point in the parameter s...

In this paper we review a number of algorithmic approaches for solving optimization problems with PDE constraints. Most of these methods were originally developed for finite dimensional problems. When applied to optimization problems with PDE constraints, new aspects become important. For instance, (discretized) PDE-constrained problems are inherently large-scale. Some aspects, like mesh indepe...

1. Introduction. Optimization problems that are constrained by partial differential equations (PDEs) arise naturally in many areas of science and engineering. In the sciences, such problems often appear as inverse problems in which some of the parameters in a simulation are unavailable, and must be estimated by comparison with physical data. These parameters are typically boundary conditions, i...