Filtern
Erscheinungsjahr
Dokumenttyp
- Dissertation (44)
- Habilitation (2)
- Wissenschaftlicher Artikel (1)
Sprache
- Englisch (47) (entfernen)
Volltext vorhanden
- ja (47) (entfernen)
Schlagworte
- Optimierung (6)
- Funktionalanalysis (5)
- Partielle Differentialgleichung (5)
- Approximation (4)
- Numerische Strömungssimulation (4)
- Shape Optimization (4)
- Approximationstheorie (3)
- Funktionentheorie (3)
- Hadamard product (3)
- Kompositionsoperator (3)
- Operatortheorie (3)
- Optimale Kontrolle (3)
- Quadratische Optimierung (3)
- Sequentielle quadratische Optimierung (3)
- Universalität (3)
- proper orthogonal decomposition (3)
- Adjungierte Differentialgleichung (2)
- Aerodynamic Design (2)
- Binomialverteilung (2)
- GPU (2)
- Gestaltoptimierung (2)
- Hadamard, Jacques (2)
- Hadamardprodukt (2)
- Homologische Algebra (2)
- Hyperzyklizität (2)
- Konvexe Optimierung (2)
- Mathematik (2)
- Monte-Carlo-Simulation (2)
- Navier-Stokes equations (2)
- Navier-Stokes-Gleichung (2)
- Nichtlineare Optimierung (2)
- Numerische Mathematik (2)
- One-Shot (2)
- Parameteridentifikation (2)
- Parameterschätzung (2)
- Robust optimization (2)
- Simulation (2)
- Strömungsmechanik (2)
- Trust-Region-Algorithmus (2)
- binomial (2)
- functional analysis (2)
- optimal control (2)
- partial integro-differential equations (2)
- universality (2)
- Adjoint Equation (1)
- Adjoint Method (1)
- Allokation (1)
- Alternierende Projektionen (1)
- Analysis (1)
- Analytisches Funktional (1)
- Arbitrage-Pricing-Theorie (1)
- Ausdehnungsoperator (1)
- Auslöschung (1)
- Banach Algebras (1)
- Banach space (1)
- Banach-Algebra (1)
- Banach-Raum (1)
- Berechnungskomplexität (1)
- Berry-Esseen (1)
- Binomial (1)
- Bregman distance (1)
- Bregman-Distanz (1)
- Brownian Motion (1)
- Brownsche Bewegung (1)
- Buehler, Robert J. (1)
- Bündel-Methode (1)
- Calibration (1)
- Cancellation (1)
- Chaotisches System (1)
- Codebuch (1)
- Combinatorial Optimization (1)
- Composition algebra (1)
- Composition operator (1)
- Computational Fluid Dynamics (1)
- Computational complexity (1)
- Convergence (1)
- Couple constraints (1)
- Decomposition (1)
- Dekomposition (1)
- Derivat <Wertpapier> (1)
- Direkte numerische Simulation (1)
- Discontinuous Galerkin (1)
- Diskontinuierliche Galerkin-Methode (1)
- Distribution (1)
- Distribution <Funktionalanalysis> (1)
- Electricity market equilibrium models (1)
- Entire Function (1)
- Error function (1)
- Ersatzmodellierung (1)
- Extensionsoperatoren (1)
- Faltungsoperator (1)
- Fehleranalyse (1)
- Fehlerfunktion (1)
- Finanzmathematik (1)
- Fledermäuse (1)
- Formenräume (1)
- Formoptimierung (1)
- Fréchet-Algebra (1)
- Functor (1)
- Funktor (1)
- Gaussian measures (1)
- Gauß-Maß (1)
- Gebietszerlegung (1)
- Gittererzeugung (1)
- Globale Konvergenz (1)
- Globale Optimierung (1)
- Graphentheorie (1)
- Graphikprozessor (1)
- Grundwasserstrom (1)
- Gärung (1)
- HPC (1)
- Hadamard cycle (1)
- Hadamardzyklus (1)
- Hassler Whitney (1)
- Hauptkomponentenanalyse (1)
- Hypercyclicity (1)
- Hypergeometrische Funktionen (1)
- Hypoelliptischer Operator (1)
- Individuenbasiertes Modell (1)
- Induktiver Limes (1)
- Innere-Punkte-Methode (1)
- Integrodifferentialgleichung (1)
- Intervallalgebra (1)
- Kegel (1)
- Kleinman (1)
- Kombinatorische Optimierung (1)
- Kompositionsalgebra (1)
- Konfidenzbereich (1)
- Konfluente hypergeometrische Funktion (1)
- Kontrolltheorie (1)
- Konvektions-Diffusionsgleichung (1)
- Konvergenz (1)
- Konvergenztheorie (1)
- Kriging (1)
- Krylov subspace methods (1)
- Krylov-Verfahren (1)
- LB-Algebra (1)
- Level Set Methode (1)
- Level constraints (1)
- Linear complementarity problems (1)
- Lineare Dynamik (1)
- Lineare Funktionalanalysis (1)
- Linearer partieller Differentialoperator (1)
- Lückenapproximation (1)
- Markov Inkrement (1)
- Markov-Kette (1)
- Matching (1)
- Matching polytope (1)
- Matrixcone (1)
- Matrixzerlegung (1)
- Mehrgitterverfahren (1)
- Mellin transformation (1)
- Mellin-Transformierte (1)
- Mesh Generation (1)
- Methode der kleinsten Quadrate (1)
- Methode der logarithmischen Barriere (1)
- Mischung (1)
- Mittag-Leffler Funktion (1)
- Mittag-Leffler function (1)
- Modellprädiktive Regelung (1)
- Monte Carlo Simulation (1)
- Monte-Carlo Methods (1)
- Multinomial (1)
- Multiplikationssatz (1)
- Nash–Cournot competition (1)
- Nebenbedingung (1)
- Newton (1)
- Newton-Verfahren (1)
- Nichtfortsetzbare Potenzreihe (1)
- Nichtglatte Optimierung (1)
- Nichtkonvexe Optimierung (1)
- Nonlinear Optimization (1)
- Normalverteilung (1)
- Numerisches Verfahren (1)
- Optimierung bei nichtlinearen partiellen Differentialgleichungen (1)
- Optimierung unter Unsicherheiten (1)
- Optimization under Uncertainty (1)
- Optionspreis (1)
- Orthogonale Zerlegung (1)
- P-Konvexität für Träger (1)
- P-Konvexität für singuläre Träger (1)
- P-convexity for singular supports (1)
- P-convexity for supports (1)
- PDE Beschränkungen (1)
- PDE Constraints (1)
- PDE-constrained optimization (1)
- POD-Methode (1)
- Parameter dependence of solutions of linear partial differential equations (1)
- Parameterabhängige Lösungen linearer partieller Differentialgeichungen (1)
- Parameterabhängigkeit (1)
- Parametrische Optimierung (1)
- Perfect competition (1)
- Polyeder (1)
- Populationsmodellierung (1)
- Projective Limit (1)
- Projektiver Limes (1)
- Proximal-Punkt-Verfahren (1)
- Quantisierung (1)
- Quantisierungkugel (1)
- Quantisierungsradius (1)
- Quantization (1)
- Rechteckwahrscheinlichkeit (1)
- Regularisierung (1)
- Regularisierungsverfahren (1)
- Rundungsfehler (1)
- Scan Statistik (1)
- Schnittebenen (1)
- Selbst-Concordanz (1)
- Semiinfinite Optimierung (1)
- Shape Kalkül (1)
- Shape SQP Methods (1)
- Shape Spaces (1)
- Spektrum <Mathematik> (1)
- Splitting (1)
- Stark stetige Halbgruppe (1)
- Statistik (1)
- Stichprobe (1)
- Stochastic Differential Equation (1)
- Stochastische Approximation (1)
- Stochastische Differentialgleichungen (1)
- Stochastische Quantisierung (1)
- Stochastische optimale Kontrolle (1)
- Stochastischer Prozess (1)
- Stratified sampling (1)
- Strukturoptimierung (1)
- Survey statistics (1)
- Taylor Shift Operator (1)
- Taylor shift operator (1)
- Theorie (1)
- Topological Algebra (1)
- Topologieoptimierung (1)
- Topologische Algebra (1)
- Topologische Algebra mit Gewebe (1)
- Topologische Sensitivität (1)
- Transaktionskosten (1)
- Transitivität (1)
- Ultradistribut (1)
- Universal functions (1)
- Universal overconvergence (1)
- Universal power series (1)
- Universelle Funktionen (1)
- Universelle Potenzreihen (1)
- Universelle Überkonvergenz (1)
- Variationsungleichung (1)
- Versuchsplanung (1)
- Vorkonditionierung (1)
- Webbed Spaces (1)
- Weingärung (1)
- Wertpapie (1)
- Whitney jets (1)
- Whitney's extension problem (1)
- Whitneys Extensionsproblem (1)
- Windkraftwerk (1)
- alternating projections (1)
- analytic functional (1)
- asymptotically optimal codebooks (1)
- asymptotisch optimale Codebücher (1)
- auxiliary problem principle (1)
- bundle-method (1)
- combinatorial optimization (1)
- completely positive (1)
- completely positive cone (1)
- complex dynamics (1)
- complexity reduction (1)
- composition operator (1)
- computational fluid dynamics (1)
- confidence region (1)
- confluent hypergeometric function (1)
- convergence (1)
- convergence theory (1)
- convolution operator (1)
- copositive cone (1)
- cutting planes (1)
- design of experiments (1)
- domain decomposition (1)
- eigenfunction expansion (1)
- extension operator (1)
- financial derivatives (1)
- flow control (1)
- ganze Funktion (1)
- gewöhnliche Differentialgleichungen (1)
- homological algebra (1)
- homological methods (1)
- homologische Methoden (1)
- hypercyclicity (1)
- hypergeometric functions (1)
- individual based model (1)
- inexact (1)
- inexact Gauss-Newton methods (1)
- kombinatorische Optimierung (1)
- komplexe Dynamik (1)
- konvexe Reforumlierungen (1)
- kopositiver Kegel (1)
- lacunary approximation (1)
- large scale problems (1)
- linear dynamics (1)
- local quantization error (1)
- logarithmic-quadratic distance function (1)
- logarithmisch-quadratische Distanzfunktion (1)
- lokaler Quantisierungsfehler (1)
- markov increment (1)
- mixing (1)
- model order reduction (1)
- model predictive control (1)
- monotone (1)
- multigrid (1)
- multinomial (1)
- n.a. (1)
- nichtnegativ (1)
- nonnegative (1)
- normal approximation (1)
- optimal continuity estimates (1)
- optimal quantization (1)
- optimale Quantisierung (1)
- optimale Stetigkeitsabschätzungen (1)
- optimization (1)
- ordinary differential equations (1)
- parameter dependence (1)
- parameter estimation (1)
- parameter identification (1)
- partial differential equations (1)
- partial differential operators of first order as generators of C0-semigroups (1)
- partial integro-differential equation (1)
- partielle Differentialgleichungen (1)
- partielle Differentialoperatoren erster Ordnung als Erzeuger von C0-Halbgruppen (1)
- partielle Integro Differentialgleichung (1)
- partielle Integro-Differentialgleichungen (1)
- partielle Integrodifferentialgleichungen (1)
- population modelling (1)
- port-Hamiltonian (1)
- preconditioning (1)
- pricing (1)
- principal component analysis (1)
- quantization ball (1)
- quantization radius (1)
- rectangular probabilities (1)
- reduced order modelling (1)
- reduced-order modelling (1)
- scan statistics (1)
- second order cone (1)
- self-concodrance (1)
- series expansion (1)
- shape calculus (1)
- shape optimization (1)
- splitting (1)
- statistics (1)
- stochastic Predictor-Corrector-Scheme (1)
- structural optimization (1)
- structure-preserving (1)
- surrogate modeling (1)
- topological derivative (1)
- topology optimization (1)
- transaction costs (1)
- transitivity (1)
- trust-region method (1)
- trust-region methods (1)
- underdetermined nonlinear least squares problem (1)
- vollständig positiv (1)
- vollständig positiver Kegel (1)
- wine fermentation (1)
- Überkonvergenz (1)
Institut
- Mathematik (47) (entfernen)
In this thesis we study structure-preserving model reduction methods for the efficient and reliable approximation of dynamical systems. A major focus is the approximation of a nonlinear flow problem on networks, which can, e.g., be used to describe gas network systems. Our proposed approximation framework guarantees so-called port-Hamiltonian structure and is general enough to be realizable by projection-based model order reduction combined with complexity reduction. We divide the discussion of the flow problem into two parts, one concerned with the linear damped wave equation and the other one with the general nonlinear flow problem on networks.
The study around the linear damped wave equation relies on a Galerkin framework, which allows for convenient network generalizations. Notable contributions of this part are the profound analysis of the algebraic setting after space-discretization in relation to the infinite dimensional setting and its implications for model reduction. In particular, this includes the discussion of differential-algebraic structures associated to the network-character of our problem and the derivation of compatibility conditions related to fundamental physical properties. Amongst the different model reduction techniques, we consider the moment matching method to be a particularly well-suited choice in our framework.
The Galerkin framework is then appropriately extended to our general nonlinear flow problem. Crucial supplementary concepts are required for the analysis, such as the partial Legendre transform and a more careful discussion of the underlying energy-based modeling. The preservation of the port-Hamiltonian structure after the model-order- and complexity-reduction-step represents a major focus of this work. Similar as in the analysis of the model order reduction, compatibility conditions play a crucial role in the analysis of our complexity reduction, which relies on a quadrature-type ansatz. Furthermore, energy-stable time-discretization schemes are derived for our port-Hamiltonian approximations, as structure-preserving methods from literature are not applicable due to our rather unconventional parametrization of the solution.
Apart from the port-Hamiltonian approximation of the flow problem, another topic of this thesis is the derivation of a new extension of moment matching methods from linear systems to quadratic-bilinear systems. Most system-theoretic reduction methods for nonlinear systems rely on multivariate frequency representations. Our approach instead uses univariate frequency representations tailored towards user-defined families of inputs. Then moment matching corresponds to a one-dimensional interpolation problem rather than to a multi-dimensional interpolation as for the multivariate approaches, i.e., it involves fewer interpolation frequencies to be chosen. The notion of signal-generator-driven systems, variational expansions of the resulting autonomous systems as well as the derivation of convenient tensor-structured approximation conditions are the main ingredients of this part. Notably, our approach allows for the incorporation of general input relations in the state equations, not only affine-linear ones as in existing system-theoretic methods.
The Hadamard product of two holomorphic functions which is defined via a convolution integral constitutes a generalization of the Hadamard product of two power series which is obtained by pointwise multiplying their coefficients. Based on the integral representation mentioned above, an associative law for this convolution is shown. The main purpose of this thesis is the examination of the linear and continuous Hadamard convolution operators. These operators map between spaces of holomorphic functions and send - with a fixed function phi - a function f to the convolution of phi and f. The transposed operator is computed and turns out to be a Hadamard convolution operator, too, mapping between spaces of germs of holomorphic functions. The kernel of Hadamard convolution operators is investigated and necessary and sufficient conditions for those operators to be injective or to have dense range are given. In case that the domain of holomorphy of the function phi allows a Mellin transform of phi, certain (generalized) monomials are identified as eigenfunctions of the corresponding operator. By means of this result and some extract of the theory of growth of entire functions, further propositions concerning the injectivity, the denseness of the range or the surjectivity of Hadamard convolution operators are shown. The relationship between Hadamard convolution operators, operators which are defined via the convolution with an analytic functional and differential operators of infinite order is investigated and the results which are obtained in the thesis are put into the research context. The thesis ends with an application of the results to the approximation of holomorphic functions by lacunary polynomials. On the one hand, the question under which conditions lacunary polynomials are dense in the space of all holomorphic functions is investigated and on the other hand, the rate of approximation is considered. In this context, a result corresponding to the Bernstein-Walsh theorem is formulated.
In this thesis, we present a new approach for estimating the effects of wind turbines for a local bat population. We build an individual based model (IBM) which simulates the movement behaviour of every single bat of the population with its own preferences, foraging behaviour and other species characteristics. This behaviour is normalized by a Monte-Carlo simulation which gives us the average behaviour of the population. The result is an occurrence map of the considered habitat which tells us how often the bat and therefore the considered bat population frequent every region of this habitat. Hence, it is possible to estimate the crossing rate of the position of an existing or potential wind turbine. We compare this individual based approach with a partial differential equation based method. This second approach produces a lower computational effort but, unfortunately, we lose information about the movement trajectories at the same time. Additionally, the PDE based model only gives us a density profile. Hence, we lose the information how often each bat crosses special points in the habitat in one night. In a next step we predict the average number of fatalities for each wind turbine in the habitat, depending on the type of the wind turbine and the behaviour of the considered bat species. This gives us the extra mortality caused by the wind turbines for the local population. This value is used for a population model and finally we can calculate whether the population still grows or if there already is a decline in population size which leads to the extinction of the population. Using the combination of all these models, we are able to evaluate the conflict of wind turbines and bats and to predict the result of this conflict. Furthermore, it is possible to find better positions for wind turbines such that the local bat population has a better chance to survive. Since bats tend to move in swarm formations under certain circumstances, we introduce swarm simulation using partial integro-differential equations. Thereby, we have a closer look at existence and uniqueness properties of solutions.
In this thesis, we aim to study the sampling allocation problem of survey statistics under uncertainty. We know that the stratum specific variances are generally not known precisely and we have no information about the distribution of uncertainty. The cost of interviewing each person in a stratum is also a highly uncertain parameter as sometimes people are unavailable for the interview. We propose robust allocations to deal with the uncertainty in both stratum specific variances and costs. However, in real life situations, we can face such cases when only one of the variances or costs is uncertain. So we propose three different robust formulations representing these different cases. To the best of our knowledge robust allocation in the sampling allocation problem has not been considered so far in any research.
The first robust formulation for linear problems was proposed by Soyster (1973). Bertsimas and Sim (2004) proposed a less conservative robust formulation for linear problems. We study these formulations and extend them for the nonlinear sampling allocation problem. It is very unlikely to happen that all of the stratum specific variances and costs are uncertain. So the robust formulations are in such a way that we can select how many strata are uncertain which we refer to as the level of uncertainty. We prove that an upper bound on the probability of violation of the nonlinear constraints can be calculated before solving the robust optimization problem. We consider various kinds of datasets and compute robust allocations. We perform multiple experiments to check the quality of the robust allocations and compare them with the existing allocation techniques.
The thesis studies the question how universal behavior is inherited by the Hadamard product. The type of universality that is considered here is universality by overconvergence; a definition will be given in chapter five. The situation can be described as follows: Let f be a universal function, and let g be a given function. Is the Hadamard product of f and g universal again? This question will be studied in chapter six. Starting with the Hadamard product for power series, a definition for a more general context must be provided. For plane open sets both containing the origin this has already been done. But in order to answer the above question, it becomes necessary to have a Hadamard product for functions that are not holomorphic at the origin. The elaboration of such a Hadamard product and its properties are the second central part of this thesis; chapter three will be concerned with them. The idea of the definition of such a Hadamard product will follow the case already known: The Hadamard product will be defined by a parameter integral. Crucial for this definition is the choice of appropriate integration curves; these will be introduced in chapter two. By means of the Hadamard product- properties it is possible to prove the Hadamard multiplication theorem and the Borel-Okada theorem. A generalization of these theorems will be presented in chapter four.
Considering the numerical simulation of mathematical models it is necessary to have efficient methods for computing special functions. We will focus our considerations in particular on the classes of Mittag-Leffler and confluent hypergeometric functions. The PhD Thesis can be structured in three parts. In the first part, entire functions are considered. If we look at the partial sums of the Taylor series with respect to the origin we find that they typically only provide a reasonable approximation of the function in a small neighborhood of the origin. The main disadvantages of these partial sums are the cancellation errors which occur when computing in fixed precision arithmetic outside this neighborhood. Therefore, our aim is to quantify and then to reduce this cancellation effect. In the next part we consider the Mittag-Leffler and the confluent hypergeometric functions in detail. Using the method we developed in the first part, we can reduce the cancellation problems by "modifying" the functions for several parts of the complex plane. Finally, in in the last part two other approaches to compute Mittag-Leffler type and confluent hypergeometric functions are discussed. If we want to evaluate such functions on unbounded intervals or sectors in the complex plane, we have to consider methods like asymptotic expansions or continued fractions for large arguments z in modulus.
In a paper of 1996 the british mathematician Graham R. Allan posed the question, whether the product of two stable elements is again stable. Here stability describes the solvability of a certain infinite system of equations. Using a method from the theory of homological algebra, it is proved that in the case of topological algebras with multiplicative webs, and thus in all common locally convex topological algebras that occur in standard analysis, the answer of Allan's question is affirmative.
In this thesis, global surrogate models for responses of expensive simulations are investigated. Computational fluid dynamics (CFD) have become an indispensable tool in the aircraft industry. But simulations of realistic aircraft configurations remain challenging and computationally expensive despite the sustained advances in computing power. With the demand for numerous simulations to describe the behavior of an output quantity over a design space, the need for surrogate models arises. They are easy to evaluate and approximate quantities of interest of a computer code. Only a few number of evaluations of the simulation are stored for determining the behavior of the response over a whole range of the input parameter domain. The Kriging method is capable of interpolating highly nonlinear, deterministic functions based on scattered datasets. Using correlation functions, distinct sensitivities of the response with respect to the input parameters can be considered automatically. Kriging can be extended to incorporate not only evaluations of the simulation, but also gradient information, which is called gradient-enhanced Kriging. Adaptive sampling strategies can generate more efficient surrogate models. Contrary to traditional one-stage approaches, the surrogate model is built step-by-step. In every stage of an adaptive process, the current surrogate is assessed in order to determine new sample locations, where the response is evaluated and the new samples are added to the existing set of samples. In this way, the sampling strategy learns about the behavior of the response and a problem-specific design is generated. Critical regions of the input parameter space are identified automatically and sampled more densely for reproducing the response's behavior correctly. The number of required expensive simulations is decreased considerably. All these approaches treat the response itself more or less as an unknown output of a black-box. A new approach is motivated by the assumption that for a predefined problem class, the behavior of the response is not arbitrary, but rather related to other instances of the mutual problem class. In CFD, for example, responses of aerodynamic coefficients share structural similarities for different airfoil geometries. The goal is to identify the similarities in a database of responses via principal component analysis and to use them for a generic surrogate model. Characteristic structures of the problem class can be used for increasing the approximation quality in new test cases. Traditional approaches still require a large number of response evaluations, in order to achieve a globally high approximation quality. Validating the generic surrogate model for industrial relevant test cases shows that they generate efficient surrogates, which are more accurate than common interpolations. Thus practical, i.e. affordable surrogates are possible already for moderate sample sizes. So far, interpolation problems were regarded as separate problems. The new approach uses the structural similarities of a mutual problem class innovatively for surrogate modeling. Concepts from response surface methods, variable-fidelity modeling, design of experiments, image registration and statistical shape analysis are connected in an interdisciplinary way. Generic surrogate modeling is not restricted to aerodynamic simulation. It can be applied, whenever expensive simulations can be assigned to a larger problem class, in which structural similarities are expected.
Industrial companies mainly aim for increasing their profit. That is why they intend to reduce production costs without sacrificing the quality. Furthermore, in the context of the 2020 energy targets, energy efficiency plays a crucial role. Mathematical modeling, simulation and optimization tools can contribute to the achievement of these industrial and environmental goals. For the process of white wine fermentation, there exists a huge potential for saving energy. In this thesis mathematical modeling, simulation and optimization tools are customized to the needs of this biochemical process and applied to it. Two different models are derived that represent the process as it can be observed in real experiments. One model takes the growth, division and death behavior of the single yeast cell into account. This is modeled by a partial integro-differential equation and additional multiple ordinary integro-differential equations showing the development of the other substrates involved. The other model, described by ordinary differential equations, represents the growth and death behavior of the yeast concentration and development of the other substrates involved. The more detailed model is investigated analytically and numerically. Thereby existence and uniqueness of solutions are studied and the process is simulated. These investigations initiate a discussion regarding the value of the additional benefit of this model compared to the simpler one. For optimization, the process is described by the less detailed model. The process is identified by a parameter and state estimation problem. The energy and quality targets are formulated in the objective function of an optimal control or model predictive control problem controlling the fermentation temperature. This means that cooling during the process of wine fermentation is controlled. Parameter and state estimation with nonlinear economic model predictive control is applied in two experiments. For the first experiment, the optimization problems are solved by multiple shooting with a backward differentiation formula method for the discretization of the problem and a sequential quadratic programming method with a line search strategy and a Broyden-Fletcher-Goldfarb-Shanno update for the solution of the constrained nonlinear optimization problems. Different rounding strategies are applied to the resulting post-fermentation control profile. Furthermore, a quality assurance test is performed. The outcomes of this experiment are remarkable energy savings and tasty wine. For the next experiment, some modifications are made, and the optimization problems are solved by using direct transcription via orthogonal collocation on finite elements for the discretization and an interior-point filter line-search method for the solution of the constrained nonlinear optimization problems. The second experiment verifies the results of the first experiment. This means that by the use of this novel control strategy energy conservation is ensured and production costs are reduced. From now on tasty white wine can be produced at a lower price and with a clearer conscience at the same time.