A Forum for the SIAM Activity Group on Optimization Volume 11 Number 2 August 2000 A Lagrange-Newton-Krylov-Schur Method for PDE-Constrained Optimization George Biros and Omar Ghattas Mechanics, Algorithms, and Computing Laboratory Department of Civil & Environmental Engineering Carnegie Mellon University, Pittsburgh, PA, USA Email: biros,oghattas @cs.cmu.edu URL: http://www.cs.cmu.edu/ ̃ gbiros...

The optimization of functions subject to partial differential equations (PDE) plays an important role in many areas of science and industry. In this paper we introduce the basic concepts of PDE-constrained optimization and show how the all-at-once approach will lead to linear systems in saddle point form. We will discuss implementation details and different boundary conditions. We then show how...

The solution of time-dependent PDE-constrained optimization problems is a challenging task in numerical analysis and applied mathematics. All-at-once discretizations and corresponding solvers provide efficient methods to robustly solve the arising discretized equations. One of the drawbacks of this approach is the high storage demand for the vectors representing the discrete space-time cylinder...

Common computational problems, such as parameter estimation in dynamic models and PDE constrained optimization, require data fitting over a set of auxiliary parameters subject to physical constraints over an underlying state. Naive quadratically penalized formulations, commonly used in practice, suffer from inherent ill-conditioning. We show that surprisingly the so-called partial minimization ...

We derive an efficient solution method for ill-posed PDE-constrained optimization problems with total variation regularization. This regularization technique allows discontinuous solutions, which is desirable in many applications. Our approach is to adapt the split Bregman technique to handle such PDE-constrained optimization problems. This leads to an iterative scheme where we must solve a lin...

Abstract. This paper provides a detailed analysis of a primal-dual interior-point method for PDE-constrained optimization. Considered are optimal control problems with control constraints in L. It is shown that the developed primal-dual interior-point method converges globally and locally superlinearly. Not only the easier L-setting is analyzed, but also a more involved L-analysis, q < ∞, is pr...

Optimization problems involving millions of variables arise in three classes of applications: optimal control, inverse problems and shape optimization. In all these cases the simulation requires the solution of 3D partialdifferential equations, which must be peformed using parallel computing environments. We will present case studies illustrating the state-of-the-art of this field, which is oft...

Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 28 May 2020Accepted: 04 June 2021Published online: 19 August 2021KeywordsPDE-constrained optimization, matrix equation, rational Krylov subspaceAMS Subject Headings65F10, 49M41, 65F45, 65F55Publication DataISSN (print): 1064-8275ISSN (online): 1095-7197Publisher: Society ...

In this paper we propose an algorithm for the bi-level optimal input design involving a parameter-dependent evolution problem. inner cycle control is fixed and parameter optimized in order to minimize cost function that measure discrepancy from some data. outer found now suitable of uncertainty parameters. The uses trust-region reduced basis approximation model with creation enrichment on-the-f...