TY - JOUR A1 - Krug, Richard A1 - Leugering, Günter A1 - Martin, Alexander A1 - Schmidt, Martin A1 - Weninger, Dieter T1 - Time-Domain Decomposition for Optimal Control Problems Governed by Semilinear Hyperbolic Systems with Mixed Two-Point Boundary Conditions JF - Control and Cybernetics N2 - In this article, we continue our work (Krug et al., 2021) on time-domain decomposition of optimal control problems for systems of semilinear hyperbolic equations in that we now consider mixed two-point boundary value problems and provide an in-depth well-posedness analysis. The more general boundary conditions significantly enlarge the scope of applications, e.g., to hyperbolic problems on metric graphs with cycles. We design an iterative method based on the optimality systems that can be interpreted as a decomposition method for the original optimal control problem into virtual control problems on smaller time domains. KW - Time-domain decomposition KW - Optimal control KW - Semilinear hyperbolic systems KW - Convergence Y1 - 2021 ER - TY - JOUR A1 - Kleinert, Thomas A1 - Manns, Julian A1 - Schmidt, Martin A1 - Weninger, Dieter T1 - Presolving Linear Bilevel Optimization Problems JF - EURO Journal on Computational Optimization N2 - Linear bilevel optimization problems are known to be strongly NP-hard and the computational techniques to solve these problems are often motivated by techniques from single-level mixed-integer optimization. Thus, during the last years and decades many branch-and-bound methods, cutting planes, or heuristics have been proposed. On the other hand, there is almost no literature on presolving linear bilevel problems although presolve is a very important ingredient in state-of-the-art mixed-integer optimization solvers. In this paper, we carry over standard presolve techniques from single-level optimization to bilevel problems and show that this needs to be done with great caution since a naive application of well-known techniques does often not lead to correctly presolved bilevel models. Our numerical study shows that presolve can also be very beneficial for bilevel problems but also highlights that these methods have a more heterogeneous effect on the solution process compared to what is known from single-level optimization. As a side result, our numerical experiments reveal that there is an urgent need for better and more heterogeneous test instance libraries to further propel the field of computational bilevel optimization. KW - Linear Bilevel Optimization KW - Presolve KW - Computational Analysis Y1 - 2021 U6 - https://doi.org/10.1016/j.ejco.2021.100020 IS - 9 ER - TY - JOUR A1 - Krug, Richard A1 - Leugering, Günter A1 - Martin, Alexander A1 - Schmidt, Martin A1 - Weninger, Dieter T1 - Time-Domain Decomposition for Optimal Control Problems Governed by Semilinear Hyperbolic Systems JF - SIAM Journal on Control and Optimization N2 - In this article, we extend the time-domain decomposition method described by Lagnese and Leugering (2003) to semilinear optimal control problems for hyperbolic balance laws with spatio-temporal varying coefficients. We provide the design of the iterative method applied to the global first-order optimality system, prove its convergence, and derive an a posteriori error estimate. The analysis is done entirely on the continuous level. A distinguishing feature of the method is that the decomposed optimality system can be interpreted as an optimality system of a local "virtual" optimal control problem. Thus, the iterative time-domain decomposition of the optimality system can be interpreted as an iterative parallel scheme for virtual optimal control problems on the subintervals. A typical example and further comments are given to show the range of potential applications. Moreover, we provide some numerical experiments to give a first interpretation of the role of the parameters involved in the iterative process. KW - Time-domain decomposition KW - Optimal control KW - Semilinear hyperbolic systems KW - Convergence KW - A posteriori error estimates Y1 - 2020 ER - TY - JOUR A1 - Bärmann, Andreas A1 - Liers, Frauke A1 - Martin, Alexander A1 - Merkert, Maximilian A1 - Thurner, Christoph A1 - Weninger, Dieter T1 - Solving network design problems via iterative aggregation JF - Mathematical Programming Computation N2 - In this work, we present an exact approach for solving network design problems that is based on an iterative graph aggregation procedure. The scheme allows existing preinstalled capacities. Starting with an initial aggregation, we solve a sequence of network design master problems over increasingly fine-grained representations of the original network. In each step, a subproblem is solved that either proves optimality of the solution or gives a directive where to refine the representation of the network in the subsequent iteration. The algorithm terminates with a globally optimal solution to the original problem. Our implementation uses a standard integer programming solver for solving the master problems as well as the subproblems. The computational results on random and realistic instances confirm the profitable use of the iterative aggregation technique. The computing time often reduces drastically when our method is compared to solving the original problem from scratch. KW - Aggregation KW - Network design KW - Combinatorial optimization KW - Mixed-integer programming KW - Branch-and-cut Y1 - 2015 U6 - https://doi.org/10.1007/s12532-015-0079-1 VL - 7 IS - 2 SP - 189 EP - 217 ER -