Fast active thermal cloaking through PDE-constrained optimization and reduced-order modelling

Reduced-Order Galerkin Approximations in PDE Constrained Optimization

Model Order Reduction for PDE Constrained Optimization

The optimization and control of systems governed by partial differential equations (PDEs) usually requires numerous evaluations of the forward problem or the optimality system. Despite the fact that many recent efforts, many of which are reported in this book, have been made to limit or reduce the number of evaluations to 5–10, this cannot be achieved in all situations and even if this is possi...

Reduced Order Constrained Optimization (ROCO):

Purpose: We use reduced-order constrained optimization (ROCO) to create clinically acceptable IMRT plans quickly and automatically for advanced lung cancer patients. Our new ROCO implementation works with the treatment planning system and full dose calculation used at Memorial Sloan-Kettering Cancer Center, and we have implemented mean dose hard-constraints, along with the point-dose and dose-v...

Multiobjective PDE-constrained optimization using the reduced-basis method

In this paper the reduced basis method is utilized to solve multiobjective optimization problems governed by linear variational equations. These problems often arise in practical applications, where the quality of the system behavior has to be measured by more than one criterium. For the numerical solution the weighting sum method is applied. This approach leads to an algorithm, where many para...

Progressive construction of a parametric reduced-order model for PDE-constrained optimization

An adaptive approach to using reduced-order models as surrogates in PDE-constrained optimization is introduced that breaks the traditional offline-online framework of model order reduction. A sequence of optimization problems constrained by a given Reduced-Order Model (ROM) is defined with the goal of converging to the solution of a given PDE-constrained optimization problem. For each reduced o...