@incollection{PickenhainLykina, author = {Pickenhain, Sabine and Lykina, Valeriya}, title = {Sufficiency conditions for infinite horizon optimal control problems}, language = {en} } @inproceedings{PickenhainLykina, author = {Pickenhain, Sabine and Lykina, Valeriya}, title = {Budget-Constrained Infinite horizon Optimal Control Problems with Linear Dynamics}, series = {55th IEEE Conference on Decision and Control, Las Vegas}, booktitle = {55th IEEE Conference on Decision and Control, Las Vegas}, publisher = {IEEE}, address = {Piscataway, NJ}, isbn = {978-1-5090-1837-6}, doi = {10.1109/CDC.2016.7798543}, pages = {1906 -- 1911}, language = {en} } @inproceedings{Lykina, author = {Lykina, Valeriya}, title = {Existence Theorem for Infinite Horizon Optimal Control Problems with Mixed Control-State Isoperimetrical Constraint}, series = {Large-Scale Scientific Computing, 11th International Conference, LSSC 2017, Sozopol, Bulgaria, June 5-9, 2017}, booktitle = {Large-Scale Scientific Computing, 11th International Conference, LSSC 2017, Sozopol, Bulgaria, June 5-9, 2017}, publisher = {Springer}, address = {Cham}, isbn = {978-3-319-73440-8}, doi = {10.1007\%2F978-3-319-73441-5_24}, pages = {228 -- 236}, abstract = {In this paper a class of infinite horizon optimal control problems with a mixed control-state isoperimetrical constraint, also interpreted as a budget constraint, is considered. Herein a linear both in the state and in the control dynamics is allowed. The problem setting includes a weighted Sobolev space as the state space. For this class of problems, we establish an existence theorem. The proved theoretical result is applied to a mixed control-state budget constrained advertisement model.}, language = {en} } @techreport{MehicicEberhardtSchrapeKrauseetal., author = {Mehicic-Eberhardt, Sana and Schrape, Stefanie and Krause, Lars and Vadachkoriya, Sofiya and Lebedynska, Yuliya and M{\"o}ller, Sarah and Lykina, Valeriya}, title = {Risikodefinition aus verschiedenen Anwendungssichten - Diskussionspapier der Fachklasse "Modelle, Methoden und Werkzeuge zum Risikomanagement" der International Graduate School der BTU Cottbus}, editor = {Woll, Ralf and Albrecht, Eike and Mißler-Behr, Magdalena and Hoppe, Annette and Berger, Ulrich and Kalusche, Wolfdietrich and Pickenhain, Sabine}, publisher = {BTU, UWV Eigenverlag}, address = {Cottbus}, pages = {77}, language = {de} } @phdthesis{Lykina, author = {Lykina, Valeriya}, title = {Beitr{\"a}ge zur Theorie der Optimalsteuerungsprobleme mit unendlichem Zeithorizont}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:co1-opus-18615}, pages = {234}, language = {de} } @techreport{PickenhainLykina, author = {Pickenhain, Sabine and Lykina, Valeriya}, title = {Pontryagin Type Maximum Principle for Budget-Constrained Infinite Horizon Optimal Control Problems with Linear Dynamics}, publisher = {Brandenburgische Technische Universit{\"a}t, Mathematisches Institut}, address = {Cottbus-Senftenberg}, pages = {22}, abstract = {In this paper a class of infinite horizon optimal control problems with an isoperimetrical constraint, also interpreted as a budget constraint, is considered. Herein a linear both in the state and in the control dynamic is allowed. The problem setting includes a weighted Sobolev space as the state space. For this class of problems, we establish the necessary optimality conditions in form of a Pontryagin Type Maximum Principle including a transversality condition. The proved theoretical result is applied to a linear-quadratic regulator problem.}, language = {en} } @misc{Lykina, author = {Lykina, Valeriya}, title = {An Existence Theorem for a Class of Infinite Horizon Optimal Control Problems}, series = {Journal of Optimization Theory and Applications}, volume = {169}, journal = {Journal of Optimization Theory and Applications}, number = {1}, issn = {0022-3239}, doi = {10.1007/s10957-013-0500-8}, pages = {50 -- 73}, abstract = {In this paper, we deal with infinite horizon optimal control problems involving affine-linear dynamics and prove the existence of optimal solutions. The innovation of this paper lies in the special setting of the problem, precisely in the choice of weighted Sobolev and weighted Lebesgue spaces as the state and control spaces, respectively, which turns out to be meaningful for various problems. We apply the generalized Weierstraß theorem to prove the existence result. A lower semicontinuity theorem which is needed for that is shown under weakened assumptions.}, language = {en} } @misc{PickenhainLykina, author = {Pickenhain, Sabine and Lykina, Valeriya}, title = {Weighted functional spaces approach in infinite horizon optimal control problems: A systematic analysis of hidden opportunities and advantages}, series = {Journal of Mathematical Analysis and Applications}, volume = {454}, journal = {Journal of Mathematical Analysis and Applications}, number = {1}, issn = {0022-247X}, pages = {195 -- 218}, language = {en} } @misc{PickenhainLykina, author = {Pickenhain, Sabine and Lykina, Valeriya}, title = {Pontryagin Type Maximum Principle for budget-constrained infinite horizon optimal control problems with linear dynamics}, series = {Journal of Mathematical Analysis and Applications}, volume = {457}, journal = {Journal of Mathematical Analysis and Applications}, number = {2}, issn = {0022-247X}, pages = {1591 -- 1612}, language = {en} } @misc{PickenhainBurtchenKoloetal., author = {Pickenhain, Sabine and Burtchen, Angie and Kolo, Katharina and Lykina, Valeriya}, title = {An indirect pseudospectral method for the solution of linear-quadratic optimal control problems with infinite horizon}, series = {Optimization}, volume = {65}, journal = {Optimization}, number = {3}, issn = {0233-1934}, doi = {10.1080/02331934.2015.1014481}, pages = {609 -- 633}, language = {en} } @misc{LykinaGrass, author = {Lykina, Valeriya and Grass, Dieter}, title = {Infinite horizon cancer treatment model with isoperimetrical constraint: existence of optimal solutions and numerical analysis}, series = {International Journal of Control}, volume = {92}, journal = {International Journal of Control}, number = {6}, issn = {1366-5820}, doi = {10.1080/00207179.2017.1396362}, pages = {1401 -- 1414}, abstract = {In this paper, a class of infinite horizon optimal control problems with a mixed control-state isoperimetrical constraint, also interpreted as a budget constraint, is considered. The underlying dynamics is assumed to be affine-linear in control. The crucial idea which is followed in this paper is the choice of a weighted Sobolev space as the state space. For this class of problems, we establish an existence result and apply it to a bilinear model of optimal cancer treatment with an isoperimetrical constraint including the overall amount of drugs used during the whole therapy horizon. A numerical analysis of this model is provided by means of open source software package OCMat, which implements a continuation method for solving discounted infinite horizon optimal control problems.}, language = {en} } @incollection{WenzkeLykinaPickenhain, author = {Wenzke, Diana and Lykina, Valeriya and Pickenhain, Sabine}, title = {State and Time Transformations of Infinite Horizon Optimal Control Problems}, series = {Variational and Optimal Control Problems on Unbounded Domains (AMS)}, booktitle = {Variational and Optimal Control Problems on Unbounded Domains (AMS)}, publisher = {American Mathematical Society (AMS)}, address = {Providence, RI}, isbn = {978-1-4704-1077-3}, pages = {189 -- 208}, language = {en} } @article{LykinaPickenhainWagner, author = {Lykina, Valeriya and Pickenhain, Sabine and Wagner, M.}, title = {Different interpretations of the improper integral objective in an infinite horizon control problem}, language = {en} } @misc{PickenhainLykinaWagner, author = {Pickenhain, Sabine and Lykina, Valeriya and Wagner, Markus}, title = {On the lower semicontinuity of functionals involving Lebesgue or improper Riemann integrals in infinite horizon optimal control problems}, series = {Control and Cybernetics}, volume = {37}, journal = {Control and Cybernetics}, issn = {0324-8569}, pages = {451 -- 468}, language = {en} } @article{LykinaPickenhainWagner, author = {Lykina, Valeriya and Pickenhain, Sabine and Wagner, M.}, title = {On a resource allocation model with inifinite horizon}, language = {en} }