@article{Reemtsen, author = {Reemtsen, Rembert}, title = {Design approximation problems for linear-phase nonrecursive digital filters}, language = {en} } @article{Reemtsen, author = {Reemtsen, Rembert}, title = {Frequency and magnitude response design approximation problems for nonlinear-phase nonrecursive digital filters}, language = {en} } @article{PotchinkovReemtsen, author = {Potchinkov, Alexander and Reemtsen, Rembert}, title = {Bicriterial design of digital filters}, language = {en} } @article{GoernerPotchinkovReemtsen, author = {G{\"o}rner, Stephan and Potchinkov, Alexander and Reemtsen, Rembert}, title = {The direct solution of nonconvex nonlinear FIR filter design problems by a SIP method}, language = {en} } @article{Reemtsen, author = {Reemtsen, Rembert}, title = {FIR filter design problems of simultaneous approximation of magnitude and phase and magnitude and group delay}, language = {en} } @book{Reemtsen, author = {Reemtsen, Rembert}, title = {Lineare Optimierung : Eine Vorlesung}, publisher = {Aachen : Shaker}, isbn = {3-8265-9615-3}, language = {de} } @incollection{Reemtsen, author = {Reemtsen, Rembert}, title = {Semi-infinite programming : discretization methods}, language = {en} } @article{AlberMeedtNuesslinetal., author = {Alber, Markus and Meedt, G. and N{\"u}sslin, F. and Reemtsen, Rembert}, title = {On the degeneracy of the IMRT optimisation problem}, language = {en} } @article{GomezBofil, author = {Gomez Bofil, W.}, title = {On generic quadratic penalty embeddings for nonlinear optimization problems}, language = {en} } @misc{ReemtsenAlber, author = {Reemtsen, Rembert and Alber, Markus}, title = {Optimierungsgest{\"u}tzte Bestrahlungsplanung f{\"u}r die Krebsbehandlung}, series = {Forum der Forschung}, volume = {9}, journal = {Forum der Forschung}, number = {18}, issn = {0947-6989}, pages = {107 -- 114}, language = {de} } @article{AlberReemtsen, author = {Alber, Markus and Reemtsen, Rembert}, title = {Intensity modulated radiotherapy treatment planning by use of a barrier-penalty multiplier method}, abstract = {The use of nonlinear functions describing biological effects has recently become a major goal in connection with intensity modulated radiotherapy (IMRT) planning models for cancer treatment. In this paper, we present a new biological model for this purpose and discuss the solution of the large-scale nonlinear optimization problems originating from it. The model includes equivalent uniform dose and partial volume constraints and employs the tumor control probability as the objective. The resulting optimization problems are convex and nonconvex constrained optimization problems with several thousands of variables, for which gradients of the involved functions are available, but the computation of Hessians is numerically too costly. It is suggested to solve these problems with a barrier-penalty multiplier method by Polyak, Ben-Tal and Zibulevsky, where this algorithm is modified according to ideas which are motivated by a related Lagrangian barrier algorithm of Conn, Gould, and Toint. In particular, the subproblems in the algorithm are solved by a conjugate gradient method, since the spectrum of the Hessian of the Lagrangian at a solution of such problem indicates fast (local) convergence of the objective function values to a good approximate (locally) optimal value. Some characteristic numbers showing the average numerical performance of the algorithm are tabulated for various types of tumors and a set of 127 clinical cases in total. Its capabilities and typical behavior also are illustrated explicitly by a computed therapy plan for a difficult clinical case of a larynx tumor.}, language = {en} } @incollection{ReemtsenAlber, author = {Reemtsen, Rembert and Alber, Markus}, title = {Continuous optimization of beamlet intensities for intensity modulated photon and proton radiotheraphy.}, language = {en} }