TY - JOUR A1 - Reemtsen, Rembert T1 - Design approximation problems for linear-phase nonrecursive digital filters KW - digital filters KW - linear-phase filters KW - Remez algorithm KW - Parks-McClellan algorithm Y1 - 2002 ER - TY - JOUR A1 - Reemtsen, Rembert T1 - Frequency and magnitude response design approximation problems for nonlinear-phase nonrecursive digital filters KW - filter design KW - digital filters KW - complex approximation KW - complete systems Y1 - 2002 ER - TY - JOUR A1 - Potchinkov, Alexander A1 - Reemtsen, Rembert T1 - Bicriterial design of digital filters KW - bicriterial optimization KW - reference point approximation KW - filter design KW - digital filters KW - compromise filters Y1 - 2002 ER - TY - JOUR A1 - Görner, Stephan A1 - Potchinkov, Alexander A1 - Reemtsen, Rembert T1 - The direct solution of nonconvex nonlinear FIR filter design problems by a SIP method KW - filter design KW - SQP methods KW - semi-infinite programming KW - FIR filters Y1 - 2000 ER - TY - JOUR A1 - Reemtsen, Rembert T1 - FIR filter design problems of simultaneous approximation of magnitude and phase and magnitude and group delay KW - filter design KW - digital filters KW - simultaneous approximation KW - magnitude-phase problem KW - magnitude-group delay problem Y1 - 2001 ER - TY - BOOK A1 - Reemtsen, Rembert T1 - Lineare Optimierung : Eine Vorlesung KW - Lineare Optimierung KW - Simplex-Algorithmus KW - Innere-Punkte-Verfahren Y1 - 2001 SN - 3-8265-9615-3 PB - Aachen : Shaker ER - TY - CHAP A1 - Reemtsen, Rembert T1 - Semi-infinite programming : discretization methods KW - semi-infinite programming KW - discretization methods Y1 - 2001 ER - TY - JOUR A1 - Alber, Markus A1 - Meedt, G. A1 - Nüsslin, F. A1 - Reemtsen, Rembert T1 - On the degeneracy of the IMRT optimisation problem KW - radiation therapy planning KW - intensity modulated radiation therapy Y1 - 2002 ER - TY - JOUR A1 - Gomez Bofil, W. T1 - On generic quadratic penalty embeddings for nonlinear optimization problems Y1 - 2001 ER - TY - GEN A1 - Reemtsen, Rembert A1 - Alber, Markus T1 - Optimierungsgestützte Bestrahlungsplanung für die Krebsbehandlung T2 - Forum der Forschung Y1 - 2005 SN - 0947-6989 VL - 9 IS - 18 SP - 107 EP - 114 ER - TY - JOUR A1 - Alber, Markus A1 - Reemtsen, Rembert T1 - Intensity modulated radiotherapy treatment planning by use of a barrier-penalty multiplier method N2 - 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. KW - radiation therapy treatment planning KW - intensity modulated radiation therapy KW - IMRT KW - barrier algorithms KW - multiplier methods KW - nonlinear rescaling method KW - barrier-penalty functions Y1 - 2007 ER - TY - CHAP A1 - Reemtsen, Rembert A1 - Alber, Markus T1 - Continuous optimization of beamlet intensities for intensity modulated photon and proton radiotheraphy. Y1 - 2009 ER -