TY - GEN A1 - Felgenhauer, Ursula A1 - Wagner, Marcus T1 - Essential properties of L∞-functions T2 - Zeitschrift für Analysis und ihre Anwendungen Y1 - 1998 SN - 0232-2064 VL - 17 IS - 1 SP - 229 EP - 242 ER - TY - THES A1 - Wagner, Marcus T1 - Erweiterungen des mehrdimensionalen Pontrjaginschen Maximumprinzips auf meßbare und beschränkte sowie distributionelle Steuerungen N2 - Leipzig, Univ., Diss., 1996 Y1 - 1996 ER - TY - JOUR A1 - Pickenhain, Sabine A1 - Wagner, Marcus T1 - Piecewise Continuous Controls in Dieudonné-Rashevsky Type Problems Y1 - 2005 ER - TY - CHAP A1 - Wagner, Marcus T1 - Nonconvex relaxation properties of multidimensional control problems Y1 - 2006 ER - TY - JOUR A1 - Pickenhain, Sabine A1 - Wagner, Marcus T1 - Minimizing sequences in class-qualified deposit problems Y1 - 2006 ER - TY - THES A1 - Wagner, Marcus T1 - Mehrdimensionale Steuerungsprobelme mit quasikonvexen Integranden Y1 - 2006 PB - Cottbus : BTU ER - TY - GEN A1 - Kunisch, Karl A1 - Wagner, Marcus T1 - Optimal control of the bidomain system (III): Existence of minimizers and first-order optimality conditions T2 - ESAIM: Mathemaical Modelling and Numerical Analysis Y1 - 2013 SN - 1290-3841 VL - 47 IS - 4 SP - 1077 EP - 1106 ER - TY - GEN A1 - Franek, Lucas A1 - Franek, Marzena A1 - Maurer, Helmut A1 - Wagner, Marcus T1 - A discretization method for the numerical solution of Dieudonné-Rashevsky type problems with application to edge detection within noisy image data T2 - Optimal Control Applications and Methods Y1 - 2012 SN - 1099-1514 VL - 33 IS - 3 SP - 276 EP - 301 ER - TY - GEN A1 - Kunisch, Karl A1 - Nagaiah, Chamakuri A1 - Wagner, Marcus T1 - A parallel Newton-Krylov method for optimal control of the monodomain model in cardiac electrophysiology T2 - Computing and Visualization in Science Y1 - 2012 SN - 1433-0369 VL - 14 IS - 6 SP - 257 EP - 269 ER - TY - GEN A1 - Kunisch, Karl A1 - Wagner, Marcus T1 - Optimal control of the bidomain system (I): The monodomain approximation with the Rogers–McCulloch model T2 - Nonlinear Analysis: Real World Applications Y1 - 2012 SN - 1468-1218 VL - 13 IS - 4 SP - 1525 EP - 1550 ER - TY - GEN A1 - Wagner, Marcus T1 - A direct method for the solution of an optimal control problem arising from image registration T2 - Numerical Algebra, Control and Optimization Y1 - 2012 SN - 2155-3289 VL - 2 IS - 3 SP - 487 EP - 510 ER - TY - GEN A1 - Wagner, Marcus T1 - Quasiconvex relaxation of multimensional control problems with integrands f(t, ξ, v) T2 - ESAIM: Control, Optimisation and Calculus of Variations Y1 - 2011 VL - 17 IS - 1 SP - 190 EP - 221 ER - TY - GEN A1 - Wagner, Marcus T1 - Smoothness properties of the lower semicontinuous quasiconvex envelope T2 - Journal for analysis and its applications Y1 - 2010 SN - 1661-4534 VL - 29 IS - 4 SP - 377 EP - 400 ER - TY - GEN A1 - Angelov, Angel A1 - Wagner, Marcus T1 - Multimodal image registration by elastic matching of edge sketches via optimal control T2 - Journal of Industrial and Management Optimization (JIMO) N2 - For the problem of multimodal image registration, an optimal control approach is presented. The geometrical information of the images will be transformed into weighted edge sketches, for which a linear-elastic or hyperelastic registration will be performed. For the numerical solution of this problem, we provide a direct method based on discretization methods and large-scale optimization techniques. A comparison of a separated and a joint access for the generation of the edge sketches and the determination of the matching deformation is made. The quality of the results obtained with the optimal control method competes well with those generated by a standard variational method. KW - Multimodal image registration KW - linear-elastic and hyperelastic regularization KW - optimal control problem Y1 - 2014 U6 - https://doi.org/10.3934/jimo.2014.10.567 SN - 1547-5816 VL - 10 IS - 2 SP - 567 EP - 590 ER - TY - GEN A1 - Wagner, Marcus T1 - A Note on Gradient Young Measure Relaxation of Dieudonné-Rashevsky Type Control Problems with Integrands f(s, ξ, v) T2 - Journal of Convex Analysis N2 - We prove a relaxation theorem for multidimensional control problems of Dieudonn\'e-Rashevsky type in terms of generalized controls. The main ingredient of the proof is a characterization theorem for gradient Young measures supported on the convex control domain $K\subset \R^{nm}$, which generalizes previous work of Kinderlehrer and Pedregal. KW - Multidimensional control problem KW - minimal value KW - nonconvex relaxation KW - lower semicontinuous quasiconvex envelope Y1 - 2014 SN - 0944-6532 VL - 21 IS - 2 SP - 453 EP - 476 ER - TY - GEN A1 - Bredies, Kristian A1 - Wagner, Marcus A1 - Schubert, Christian A1 - Ahnelt, Peter T1 - Computer-assisted counting of retinal cells by automatic segmentation after TV denoising T2 - BMC ophthalmology KW - Mammalian photoreceptor cells KW - Automatical counting KW - Adaptive algorithm Y1 - 2013 U6 - https://doi.org/10.1186/1471-2415-13-59 SN - 1471-2415 VL - 13 ER - TY - GEN A1 - Kunisch, Karl A1 - Wagner, Marcus T1 - Optimal control of the bidomain system (II): uniqueness and regularity theorems for weak solutions T2 - Annali di Matematica Pura ed Applicata N2 - Motivated by the study of related optimal control problems, weak and strong solution concepts for the bidomain system together with two-variable ionic models are analyzed. A key ingredient for the analysis is the bidomain bilinear form. Global existence of weak and strong solutions as well as stability and uniqueness theorems is proven. KW - Bidomain equations KW - Weak solution Y1 - 2013 U6 - https://doi.org/10.1007/s10231-012-0254-1 SN - 0373-3114 SN - 1618-1891 VL - 192 IS - 6 SP - 951 EP - 986 ER - TY - GEN A1 - Brune, Christoph A1 - Maurer, Helmut A1 - Wagner, Marcus T1 - Detection of Intensity and Motion Edges within Optical Flow via Multidimensional Control T2 - SIAM Journal on Imaging Sciences N2 - In this paper, we propose a new optimization approach for the simultaneous computation of optical flow and edge detection therein. Instead of using an Ambrosio–Tortorelli type energy functional, we reformulate the optical flow problem as a multidimensional control problem. The optimal control problem is solved by discretization methods and large-scale optimization techniques. The edge detector can be immediately built from the control variables. We provide three series of numerical examples. The first shows that the mere presence of a gradient restriction has a regularizing effect, while the second demonstrates how to balance the regularizing effects of a term within the objective and the control restriction. The third series of numerical results is concerned with the direct evaluation of a TV-regularization term by introduction of control variables with sign restrictions. Y1 - 2009 U6 - https://doi.org/10.1137/080725064 VL - 2 IS - 4 SP - 1190 EP - 1210 ER - TY - GEN A1 - Wagner, Marcus T1 - Pontryagin’s Maximum Principle for Multidimensional Control Problems in Image Processing T2 - Journal of Optimization Theory and Applications N2 - In the present paper, we prove a substantially improved version of the Pontryagin maximum principle for convex multidimensional control problems of Dieudonné-Rashevsky type. Although the range of the operator describing the first-order PDE system involved in this problem has infinite codimension, we obtain first-order necessary conditions in a completely analogous form as in the one-dimensional case. Furthermore, the adjoint variables are subjected to a Weyl decomposition. We reformulate two basic problems of mathematical image processing (determination of optical flow and shape from shading problem) within the framework of optimal control, which gives the possibility to incorporate hard constraints in the problems. In the convex case, we state the necessary optimality conditions for these problems. KW - Multidimensional control problems KW - First-order necessary conditions KW - Image processing Y1 - 2009 U6 - https://doi.org/10.1007/s10957-008-9460-9 SN - 1573-2878 SN - 0022-3239 VL - 140 IS - 3 SP - 543 EP - 576 ER - TY - RPRT A1 - Wagner, Marcus T1 - Application of a result of Ioffe/Tichomirov to multidimensional control problems of Dieudonné-Rashevsky type Y1 - 2002 PB - Max-Planck-Institut für Mathematik in den Naturwissenschaften CY - Leipzig ER - TY - RPRT A1 - Wagner, Marcus T1 - Some extensions of Hüseinov's C∞-approximation theorem for Lipschitz functions Y1 - 2001 PB - Institut für Mathematik CY - Cottbus ER -