Christian Kirches \(\) We present randomized reconstruction approaches for optimal solutions to mixed-integer elliptic PDE control systems. Approximation properties and relations to sum-up rounding are derived using the cut norm. This enables us to dispose of space-filling curves required for sum-up rounding. Rates of almost sure convergence in the cut norm and the SUR norm in control … Read more
Mathematical modeling, simulation, and optimization can significantly support the development and characterization of chromatography steps in the biopharmaceutical industry. Particularly mechanistic models become preferably used, as these models, once carefully calibrated, can be employed for a reliable optimization. However, model calibration is a difficult task in this context due to high correlations between parameters, highly … Read more
This article is concerned with a recently proposed switching cost aware rounding (SCARP) strategy in the combinatorial integral decomposition for mixed-integer optimal control problems (MIOCPs). We consider the case of a control variable that is discrete-valued and distributed on a two-dimensional domain. While the theoretical results from the one-dimensional case directly apply to the multidimensional … Read more
We extend recent work on the performance of the combinatorial integral approximation decomposition approach for Mixed-Integer Optimal Control Problems (MIOCPs) in the presence of combinatorial constraints or switching costs on an equidistant grid. For the time discretized problem, we reformulate the emerging rounding problem in the decomposition approach as a matching problem on a bipartite … Read more
Multimodal chromatography is a powerful tool in the downstream processing of biopharmaceuticals. To fully benefit from this technology, an efficient process strategy must be determined beforehand. To facilitate this task, we employ a recent mechanistic model for multimodal chromatography, which takes salt concentration and pH into account, and we present a mathematical framework for the … Read more
We investigate an extension of Mixed-Integer Optimal Control Problems (MIOCPs) by adding switching costs, which enables the penalization of chattering and extends current modeling capabilities. The decomposition approach, consisting of solving a partial outer convexification to obtain a relaxed solution and using rounding schemes to obtain a discrete-valued control can still be applied, but the … Read more
This work continues an ongoing effort to compare non-smooth optimization problems in abs-normal form to Mathematical Programs with Complementarity Constraints (MPCCs). We study general Nonlinear Programs with equality and inequality constraints in abs-normal form, so-called Abs-Normal NLPs, and their relation to equivalent MPCC reformulations. We introduce the concepts of Abadie’s and Guignard’s kink qualification and … Read more
This work is part of an ongoing effort of comparing non-smooth optimization problems in abs-normal form to MPCCs. We study the general abs-normal NLP with equality and inequality constraints in relation to an equivalent MPCC reformulation. We show that kink qualifications and MPCC constraint qualifications of linear independence type and Mangasarian-Fromovitz type are equivalent. Then … Read more
Simulation, optimization and control of robotic and bio-mechanical systems depend on a mathematical model description, typically a rigid-body system connected by joints, for which efficient algorithms to compute the forward or inverse dynamics exist. Models that e.g.\ include spring-damper systems are subject to both kinematic and loop constraints. Gradient-based optimization and control methods require derivatives … Read more
This article investigates a class of Mixed-Integer Optimal Control Problems (MIOCPs) with switching costs. We introduce the problem class of Minimal-Switching-Cost Optimal Control Problems (MSCP) with an objective function that consists of two summands, a continuous term depending on the state vector and an encoding of the discrete switching costs. State vectors of Mixed-Integer Optimal … Read more