Christian Kirches 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
In this article, we present a framework for the numerical solution of optimal control problems, constrained by ordinary differential equations which can run in (finitely many) different modes, where a change of modes leads to additional switching cost in the cost function, and whenever the system changes its mode, jumps in the differential states are … Read more
We show that the problem of unconstrained minimization of a function in abs-normal form is equivalent to identifying a certain stationary point of a counterpart Mathematical Program with Equilibrium Constraints (MPEC). Hence, concepts introduced for the abs-normal forms turn out to be closely related to established concepts in the theory of MPECs. We give a … Read more
Partial outer convexification is a relaxation technique for MIOCPs being constrained by time-dependent differential equations. Sum-Up-Rounding algorithms allow to approximate feasible points of the relaxed, convexified continuous problem with binary ones that are feasible up to an arbitrarily small $\delta > 0$. We show that this approximation property holds for ODEs and semilinear PDEs under … Read more
Approximation algorithms like sum-up rounding that allow to compute integer-valued approximations of the continuous controls in a weak$^*$ sense have attracted interest recently. They allow to approximate (optimal) feasible solutions of continuous relaxations of mixed-integer control problems (MIOCPs) with integer controls arbitrarily close. To this end, they use compactness properties of the underlying state equation, … Read more