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A certified reduced basis method for parametrized elliptic optimal control problems

Mark Kärcher, Martin A. Grepl (2014)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper, we employ the reduced basis method as a surrogate model for the solution of linear-quadratic optimal control problems governed by parametrized elliptic partial differential equations. We present a posteriori error estimation and dual procedures that provide rigorous bounds for the error in several quantities of interest: the optimal control, the cost functional, and general linear output functionals of the control, state, and adjoint variables. We show that, based on the assumption...

A conjugate gradient method with quasi-Newton approximation

Jonas Koko (2000)

Applicationes Mathematicae

The conjugate gradient method of Liu and Storey is an efficient minimization algorithm which uses second derivatives information, without saving matrices, by finite difference approximation. It is shown that the finite difference scheme can be removed by using a quasi-Newton approximation for computing a search direction, without loss of convergence. A conjugate gradient method based on BFGS approximation is proposed and compared with existing methods of the same class.

A fast Lagrangian heuristic for large-scale capacitated lot-size problems with restricted cost structures

Kjetil K. Haugen, Guillaume Lanquepin-Chesnais, Asmund Olstad (2012)


In this paper, we demonstrate the computational consequences of making a simple assumption on production cost structures in capacitated lot-size problems. Our results indicate that our cost assumption of increased productivity over time has dramatic effects on the problem sizes which are solvable. Our experiments indicate that problems with more than 1000 products in more than 1000 time periods may be solved within reasonable time. The Lagrangian decomposition algorithm we use does of course not...

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