@misc{FelgenhauerWagner, author = {Felgenhauer, Ursula and Wagner, Marcus}, title = {Essential properties of L∞-functions}, series = {Zeitschrift f{\"u}r Analysis und ihre Anwendungen}, volume = {17}, journal = {Zeitschrift f{\"u}r Analysis und ihre Anwendungen}, number = {1}, issn = {0232-2064}, pages = {229 -- 242}, language = {en} } @phdthesis{Wagner, author = {Wagner, Marcus}, title = {Erweiterungen des mehrdimensionalen Pontrjaginschen Maximumprinzips auf meßbare und beschr{\"a}nkte sowie distributionelle Steuerungen}, abstract = {Leipzig, Univ., Diss., 1996}, language = {de} } @article{PickenhainWagner, author = {Pickenhain, Sabine and Wagner, Marcus}, title = {Piecewise Continuous Controls in Dieudonn{\´e}-Rashevsky Type Problems}, language = {en} } @incollection{Wagner, author = {Wagner, Marcus}, title = {Nonconvex relaxation properties of multidimensional control problems}, language = {en} } @article{PickenhainWagner, author = {Pickenhain, Sabine and Wagner, Marcus}, title = {Minimizing sequences in class-qualified deposit problems}, language = {en} } @phdthesis{Wagner, author = {Wagner, Marcus}, title = {Mehrdimensionale Steuerungsprobelme mit quasikonvexen Integranden}, publisher = {Cottbus : BTU}, language = {de} } @misc{KunischWagner, author = {Kunisch, Karl and Wagner, Marcus}, title = {Optimal control of the bidomain system (III): Existence of minimizers and first-order optimality conditions}, series = {ESAIM: Mathemaical Modelling and Numerical Analysis}, volume = {47}, journal = {ESAIM: Mathemaical Modelling and Numerical Analysis}, number = {4}, issn = {1290-3841}, pages = {1077 -- 1106}, language = {en} } @misc{FranekFranekMaureretal., author = {Franek, Lucas and Franek, Marzena and Maurer, Helmut and Wagner, Marcus}, title = {A discretization method for the numerical solution of Dieudonn{\´e}-Rashevsky type problems with application to edge detection within noisy image data}, series = {Optimal Control Applications and Methods}, volume = {33}, journal = {Optimal Control Applications and Methods}, number = {3}, issn = {1099-1514}, pages = {276 -- 301}, language = {en} } @misc{KunischNagaiahWagner, author = {Kunisch, Karl and Nagaiah, Chamakuri and Wagner, Marcus}, title = {A parallel Newton-Krylov method for optimal control of the monodomain model in cardiac electrophysiology}, series = {Computing and Visualization in Science}, volume = {14}, journal = {Computing and Visualization in Science}, number = {6}, issn = {1433-0369}, pages = {257 -- 269}, language = {en} } @misc{KunischWagner, author = {Kunisch, Karl and Wagner, Marcus}, title = {Optimal control of the bidomain system (I): The monodomain approximation with the Rogers-McCulloch model}, series = {Nonlinear Analysis: Real World Applications}, volume = {13}, journal = {Nonlinear Analysis: Real World Applications}, number = {4}, issn = {1468-1218}, pages = {1525 -- 1550}, language = {en} } @misc{Wagner, author = {Wagner, Marcus}, title = {A direct method for the solution of an optimal control problem arising from image registration}, series = {Numerical Algebra, Control and Optimization}, volume = {2}, journal = {Numerical Algebra, Control and Optimization}, number = {3}, issn = {2155-3289}, pages = {487 -- 510}, language = {en} } @misc{Wagner, author = {Wagner, Marcus}, title = {Quasiconvex relaxation of multimensional control problems with integrands f(t, ξ, v)}, series = {ESAIM: Control, Optimisation and Calculus of Variations}, volume = {17}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, number = {1}, pages = {190 -- 221}, language = {en} } @misc{Wagner, author = {Wagner, Marcus}, title = {Smoothness properties of the lower semicontinuous quasiconvex envelope}, series = {Journal for analysis and its applications}, volume = {29}, journal = {Journal for analysis and its applications}, number = {4}, issn = {1661-4534}, pages = {377 -- 400}, language = {en} } @misc{AngelovWagner, author = {Angelov, Angel and Wagner, Marcus}, title = {Multimodal image registration by elastic matching of edge sketches via optimal control}, series = {Journal of Industrial and Management Optimization (JIMO)}, volume = {10}, journal = {Journal of Industrial and Management Optimization (JIMO)}, number = {2}, issn = {1547-5816}, doi = {10.3934/jimo.2014.10.567}, pages = {567 -- 590}, abstract = {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.}, language = {en} } @misc{Wagner, author = {Wagner, Marcus}, title = {A Note on Gradient Young Measure Relaxation of Dieudonn{\´e}-Rashevsky Type Control Problems with Integrands f(s, ξ, v)}, series = {Journal of Convex Analysis}, volume = {21}, journal = {Journal of Convex Analysis}, number = {2}, issn = {0944-6532}, pages = {453 -- 476}, abstract = {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.}, language = {en} } @misc{BrediesWagnerSchubertetal., author = {Bredies, Kristian and Wagner, Marcus and Schubert, Christian and Ahnelt, Peter}, title = {Computer-assisted counting of retinal cells by automatic segmentation after TV denoising}, series = {BMC ophthalmology}, volume = {13}, journal = {BMC ophthalmology}, issn = {1471-2415}, doi = {10.1186/1471-2415-13-59}, language = {en} } @misc{KunischWagner, author = {Kunisch, Karl and Wagner, Marcus}, title = {Optimal control of the bidomain system (II): uniqueness and regularity theorems for weak solutions}, series = {Annali di Matematica Pura ed Applicata}, volume = {192}, journal = {Annali di Matematica Pura ed Applicata}, number = {6}, issn = {0373-3114}, doi = {10.1007/s10231-012-0254-1}, pages = {951 -- 986}, abstract = {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.}, language = {en} } @misc{BruneMaurerWagner, author = {Brune, Christoph and Maurer, Helmut and Wagner, Marcus}, title = {Detection of Intensity and Motion Edges within Optical Flow via Multidimensional Control}, series = {SIAM Journal on Imaging Sciences}, volume = {2}, journal = {SIAM Journal on Imaging Sciences}, number = {4}, doi = {10.1137/080725064}, pages = {1190 -- 1210}, abstract = {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.}, language = {en} } @misc{Wagner, author = {Wagner, Marcus}, title = {Pontryagin's Maximum Principle for Multidimensional Control Problems in Image Processing}, series = {Journal of Optimization Theory and Applications}, volume = {140}, journal = {Journal of Optimization Theory and Applications}, number = {3}, issn = {1573-2878}, doi = {10.1007/s10957-008-9460-9}, pages = {543 -- 576}, abstract = {In the present paper, we prove a substantially improved version of the Pontryagin maximum principle for convex multidimensional control problems of Dieudonn{\´e}-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.}, language = {en} } @techreport{Wagner, author = {Wagner, Marcus}, title = {Application of a result of Ioffe/Tichomirov to multidimensional control problems of Dieudonn{\´e}-Rashevsky type}, publisher = {Max-Planck-Institut f{\"u}r Mathematik in den Naturwissenschaften}, address = {Leipzig}, pages = {12}, language = {en} } @techreport{Wagner, author = {Wagner, Marcus}, title = {Some extensions of H{\"u}seinov's C∞-approximation theorem for Lipschitz functions}, publisher = {Institut f{\"u}r Mathematik}, address = {Cottbus}, pages = {8}, language = {en} }