pde-constrained optimization – Page 2

pyomo.dae: A Modeling and Automatic Discretization Framework for Optimization with Differential and Algebraic Equations

Published: 2016/05/25

Modeling Languages and Systems, Optimization of Systems modeled by PDEs, Systems governed by Differential Equations Optimization algebraic modeling language, dae constrained optimization, dynamic programming, mathematical modeling, pde-constrained optimization

We describe pyomo.dae, an open source Python-based modeling framework that enables high-level abstract specification of optimization problems with differential and algebraic equations. The pyomo.dae framework is integrated with the Pyomo open source algebraic modeling language, and is available at http: //www.pyomo.org. One key feature of pyomo.dae is that it does not restrict users to standard, … Read more

A Note on the Implementation of an Interior-Point Algorithm for Nonlinear Optimization with Inexact Step Computations

Published: 2011/04/15, Updated: 2014/05/31

Frank E. Curtis

Johannes Huber

Olaf Schenk

Constrained Nonlinear Optimization inexact linear system solvers, interior point methods, krylov subspace methods, large-scale optimization, line-search, nonconvex optimization, pde-constrained optimization, trust-region methods

This paper describes an implementation of an interior-point algorithm for large-scale nonlinear optimization. It is based on the algorithm proposed by Curtis et al. (SIAM J Sci Comput 32:3447–3475, 2010), a method that possesses global convergence guarantees to first-order stationary points with the novel feature that inexact search direction calculations are allowed in order to … Read more

Automatically Assessing the Performance of an Optimization-Based Multigrid Method

Published: 2008/05/02

Robert Michael Lewis

Stephen G. Nash

Systems governed by Differential Equations Optimization multigrid methods, optimization of systems governed by differential equations, pde-constrained optimization

Many large nonlinear optimization problems are based upon discretizations of underlying function spaces. Optimization-based multigrid methods—that is, multigrid methods based on solving coarser versions of an optimization problem—are designed to solve such discretized problems efficiently by taking explicit advantage of the family of discretizations. The methods are generalizations of more traditional multigrid methods for solving … Read more

Data Assimilation in Weather Forecasting: A Case Study in PDE-Constrained Optimization

Published: 2007/02/14

Nonlinear Optimization, Optimization of Systems modeled by PDEs nonlinear programming, pde-constrained optimization

Variational data assimilation is used at major weather prediction centers to produce the initial conditions for 7- to 10-day weather forecasts. This technique requires the solution of a very large data-fitting problem in which the major element is a set of partial differential equations that models the evolution of the atmosphere over a time window … Read more

Primal-dual interior point methods for PDE-constrained optimization

Published: 2006/04/24

Michael Ulbrich

Stefan Ulbrich

Constrained Nonlinear Optimization, Infinite Dimensional Optimization, Systems governed by Differential Equations Optimization global convergence, infinite dimensional optimization, interior point methods, optimal control, pde-constrained optimization, superlinear local convergence

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 $L^p$. It is shown that the developed primal-dual interior-point method converges globally and locally superlinearly. Not only the easier $L^\infty$-setting is analyzed, but also a more involved $L^q$-analysis, $q