Dr. rer. nat. Torsten Bosse Scientist

Basic Info About Me


I'm just an average guy doing average things in an average world ... NOT. If I am not lost in my small math world thinking about piecewise linear algebra, algorithmic differentiation, nonlinear optimization, HPC, and simulations chances are high that you can find me paddling on my SUP, riding my motorbike, playing some billard, making a mess in my kitchen, working on one of my projects, or simply discovering new playgrounds in Berlin with my son.










Best son in the world.

My mum

CEO at Family Business

Most loving math nerd and brother.

My sister

CEO at Family Business

A true inspiring leader for the next generation.

My dad

CBDO at Family Business

Best game developer and creative person.

My son

CCO at Family Business

My Resume

  • Scientific career

  • 1992-2001

    GHE entrance qualification

    @KCG Königin-Charlotte-Gymnasium, Stuttgart, Germany

  • 2001-2002

    Civil Service

    Malteser - Stuttgart, Germany

  • 2002-2009

    Dipl. Math.

    @HUB Humboldt-University of Berlin, Germany

  • 2010-2014

    Dr. rer. nat.

    @HUB Humboldt-University of Berlin, Germany

  • 2014-2016

    Wilkinson Post-doc

    @ANL Argonne National Laboratory, Illinois, US

  • 2017-dato


    @FSU Friedrich-Schiller-University Jena, Germany

  • Projects

  • 2008-2009


    @DFG Program MATHEON

    C12 General Purpose, Linearly Invariant Algorithm for Large-Scale Non-linear Programming

  • 2010-2012


    @DFG Priority Program

    SPP 1253 - Automated Extension of Fixed Point PDE Solvers for Optimal Design with Bounded Retardation

  • 2018


    @Thüringer Aufbaubank

    DAWI - Zusammenführung von Datenmanagement und -analyse in datengetriebenen Wissenschaften

  • 2019-2020


    @DFG Collaborative Research Centre

    SFB TRR 166 - ReceptorLight- Hochleistungs-Lichtmikroskopie zur Aufklärung der Funktion von Membranrezeptoren

  • 2021-dato



    THInKI - Thüringer Hochschulinitiative für KI im Studium

  • 2021-dato


    @Carl Zeiss Foundation

    Interactive Inference - Scientific Breakthroughs in AI

My Research Directions

Modelling and Simulations

Algorithmic Differentiation

Piecewise Linear Algebra

Optimization Methods

High-performance Computing

Machine Learning

My Skills









Computer Science




My Publications

A short summary of my scientific publications.
Feel free to contact me in case of questions.

Checkpointing for piecewise smooth functions

  • T. Bosse, F. Taubert, and M. Bücker
  • 2021
  • DOI: Preprint

Check-pointing (CP) is a standard technique in Algorithmic Differentiation and high performance computing to reduce memory costs in trade-off for additional computational overhead. The basic idea of CP is to reduce memory requirements by not storing all information but only some intermediate values within the original computation, which can be used to recompute other values required by some later computations. In this paper, we present an off-line, synchronous, out-of-core check-pointing ... Read more

Local models of piecewise normal forms

  • T.Bosse and M.Bücker
  • 2021
  • DOI: Preprint

Algorithmic differentiation allows the approximation of certain non-smooth functions by piecewise affine models. In contrast to linear models, these models are usually more accurate approximations since they reflect underlying non-smoothness. However, the algebraic representation of the piecewise affine models can be come large and, thus, computationally inefficient. As a solution, we propose to approximate the piecewise affine approximation by local models that have a smaller algebraic ... Read more

Efficient signed backward substitution for piecewise affine functions via path problems in a directed acyclic graph

  • T. Bosse, R.Seidler, and M. Bücker
  • 2021
  • DOI: 10.1137/1.9781611976830.16

We introduce an efficient signed backward substitution for a highly-structured system. More precisely, the problem is to find a vector u of dimension s that solves the system of piecewise affine equations u = c + L|u|, where L is a strictly lower left triangular s times s matrix, c denotes a given vector of dimension s, and the notation |cdot| indicates the component-wise absolute value of a vector. The novel approach is based on a Neumann series reformulation and attempts to exploit a high ... Read more

Evaluation of dense Abs-Normal Forms on GPUs

  • T.Bosse, R.Seidler, K.Kiedom
  • 2019
  • DOI: Preprint

In the last decades several highly efficient linear algebra systems have been developed, which became an essential part in scientific computing. Only minor attention has been spend on the numerical evaluation and the solution of piecewise linear systems. In this paper, we address this problem and focus on the efficient evaluation of piecewise linear functions in Abs-Normal Form (ANF). Therefore, four different methods are presented that partly exploit parallelism. For all methods, we discuss ... Read more

Study of the numerical efficiency of structured abs-normal forms

  • T.Bosse and S. Narayanan
  • 2019
  • DOI: 10.1080/10556788.2019.1613654A

The abs-normal form (ANF) can be used to represent almost any piecewise linear function. Several of these piecewise linear functions exhibit a certain structure that has an impact on the numerical efficiency of the ANF representation. In this paper, three common structures are investigated that typically arise in applications and require special numerical treatment: the sum, the composition, and the componentwise maximum/minimum of several functions. For these structures, the ... Read more

(Almost) Matrix-free solver for piecewise linear functions in Abs-Normal form

  • T.Bosse
  • 2019
  • DOI: 10.1002/nla.2258

The abs-normal form (ANF) is a compact algebraic representation for piecewise linear functions. These functions can be used to approximate piecewise smooth functions and contain valuable information about the non-smoothness of the investigated function. The information help to define step directions within general Newton methods that obey the structure of the original function and typically yield better convergence. However, the computation of the generalized Newton directions requires the ... Read more

Augmenting the one-shot framework by additional constraints

  • T. Bosse
  • 2016
  • DOI: 10.1080/10556788.2016.1180692

The (multistep) one-shot method for design optimization problems has been successfully implemented for various applications. To this end, a slowly convergent primal fixed-point iteration of the state equation is augmented by an adjoint iteration and a corresponding preconditioned design update. In this paper we present a modification of the method that allows for additional equality constraints besides the usual state equation. A retardation analysis and the local convergence of the method in ... Read more

On lipschitz optimization based on gray-box piecewise linearization

  • A. Griewank, A. Walther, S. Fiege, and T.Bosse
  • 2015
  • DOI: 10.1007/s10107-015-0934-x

We address the problem of minimizing objectives from the class of piecewise differentiable functions whose nonsmoothness can be encapsulated in the absolute value function. They possess local piecewise linear approximations with a discrepancy that can be bounded by a quadratic proximal term. This overestimating local model is continuous but generally nonconvex. It can be generated in its abs-normal form by a minor extension of standard algorithmic differentiation tools. Here we demonstrate how ... Read more

An algorithm for pointwise evaluation of polyconvex envelopes II: Generalization and numerical results

  • T. Bosse, L. Eneya, and A. Griewank
  • 2015
  • DOI: 10.1007/s13370-013-0181-3

In the first part of this paper (Afrika Matematika 1–24, 2011) we introduced a method for computing the value of a polyconvex envelope at a given feed A0∈Rm×n. The method generalizes an approach for computing convex envelopes proposed by Michelsen (Fluid Phase Equilibria 9:1–19 1982; Fluid Phase Equilibria 9:21–40 1982), and later implemented by McKinnon and Mongeau (J Optim Glob 12(4):325–351, 1998). While alternating between a local and a global optimization phase, Lagrange ... Read more

Multigrid method for nonsmooth problems using a Total quasi-Newton Approach

  • T.Bosse
  • 2015
  • DOI: Preprint

Multigrid methods have been shown to be an effcient tool for solving partial differential equations. In this paper, the idea of a multigrid method for nonsmooth problems is presented based on techniques from piecewise linear differentiation. In detail, the original nonsmooth problem is approximated by a sequence of piecewise linear models, which can be written in abs-normal form by using additional switching variables. In certain cases, one can exploit the structure of the piecewise ... Read more

One-shot approaches to design optimzation

  • T. Bosse, N. Gauger, A. Griewank, S. Günther, and
  • 2014
  • DOI: 10.1007/978-3-319-05083-6_5

The paper describes general methodologies for the solution of design optimization problems. In particular we outline the close relations between a fixed point solver based piggy back approach and a Reduced SQP method in Jacobi and Seidel variants. The convergence rate and general efficacy is shown to be strongly dependent on the characteristics of the state equation and the objective function. In the QP scenario where the state equation is linear and the objective quadratic, finite termination ... Read more

Optimal Design with Bounded Retardation for Problems with Non-separable Adjoints

  • T. Bosse, N. Gauger, A. Griewank, S. Günther, L. K
  • 2014
  • DOI: 10.1007/978-3-319-05083-6_6

For many real world processes there are mathematical models in terms of PDEs. However, for most of the applications any analytical solution is out of reach. Therefore, numerous simulation codes depending on some design parameters have been developed and implemented. In our research we focus on the transition from such simulation codes to optimization, where the design parameters are chosen in such a way that the underlying model is optimal with respect to some measure. In contrast to general ... Read more

Nonlinear programming with applications to production processes

  • T. Bosse, A. Griewank, R. Henrion, D. Hömberg, C.
  • 2014
  • DOI: 10.4171/137

Nonlinear programming is a key technology for finding optimal decisions in production processes. It applies to optimal control as well as to operations research, to deterministic as well as to stochastic models. The efficient solution of nonlinear programs requires both, a good structural understanding of the underlying optimization problems and the use of tailored algorithmic approaches mainly based on SQP methods. The present chapter provides an account of the work in three MATHEON-projects ... Read more

Optimal control of beer fermentation processes with Lipschitz-constraint on the control

  • T. Bosse and A. Griewank
  • 2014
  • DOI: 10.1002/jib.150

Nowadays, one can find in almost all industrial products a trail of mathematical optimization. In particular, the theory and algorithms of optimal control have helped in various fields to reduce the production time and to improve the quality of the considered products. As a special class of applications, two optimal control formulations for the fermentation process of beer are presented. The reactions of the fermentation processes are modelled by a system of ordinary differential equations that ... Read more

Cubic overestimation and secant updating for unconstrained optimization of C2,1 functions

  • T. Bosse, J. Fischer, and A. Griewank
  • 2014
  • DOI: 10.1080/10556788.2013.863308

The discrepancy between an objective function f and its local quadratic model f(x)+∇ f(x)⊤ s+s⊤ H(x) s/2 ≈ f(x+s) at the current iterate x is estimated using a cubic term q |s|3/3. Potential steps are chosen such that they minimize (or at least significantly reduce) the overestimating function ∇ f(x)⊤ s+s⊤ B s/2+q |s|3/3 with B ≈ H(x). This ensures f(x+s)0 is too small. Either one or ... Read more

Adaptive sequencing of primal, dual, and design steps in simulation based optimization

  • T. Bosse, L. Lehmann, and A. Griewank
  • 2014
  • DOI: 10.1007/s10589-013-9606-z

Many researchers have used Oneshot optimization methods based on user-specified primal state iterations, the corresponding adjoint iterations, and appropriately preconditioned design steps. Our goal here is to develop heuristics for sequencing these three subtasks, in order to optimize the convergence rate of the resulting coupled iteration cycle. A key ingredient is the preconditioning in the design step by a BFGS approximation of the projected Hessian. We provide a hard bound on the spectral ... Read more

Numerical Optimization of a Simulated Moving Bed Process using a Total quasi-Newton Approach

  • T.Bosse, A. Ziessler, and A. Griewank
  • 2013
  • DOI: Preprint

The CUTEr test set is often used to verify the robustness and performance of non-linear optimization solvers. In our experiments it was observed that the total quasi-Newton solver LRAMBO achieves no reduction/improvement when contstraint Jacobians are cheap to evaluate and easy to factorize, which is true for practically all problems in the CUTEr test set. This makes the use of optimization algorithms exclusively based on low rank updates and evaluating derivative vectors somewhat slower than ... Read more

The Relative Cost of Function and Derivative Evaluations in the CUTEr Test Set

  • T. Bosse and A. Griewank
  • 2012
  • DOI: 10.1007/978-3-642-30023-3_21

The CUTEr test set represents a testing environment for nonlinear optimization solvers containing more than 1,000 academic and applied nonlinear problems. It is often used to verify the robustness and performance of nonlinear optimization solvers. In this paper, we perform a quantitative analysis of the CUTEr test set. As a result we see that some paradigms of nonlinear optimization and automatic differentiation can be verified whereas others need to be questioned. Furthermore, we show that the ... Read more

Die magische Quadratur des Superhirns

  • T. Bosse, A.Griewank, L.Lehmann, and D.Schlagk
  • 2012
  • DOI: 10.1515/dmvm-2012-0015

Die von Robin Wersig in der ZDF Sendung „Deutschland’s Superhirn 2011“ am 28. Dezember 2011 behandelte Aufgabe wird mathematisch formuliert und ihre – in gewissem Sinne – minimale Lösung beschrieben. Diese beruht auf einer 1858 veröffentlichten magischen Springertour über das Schachbrett von Jänisch. Die Kenntnis dieses geometrisch einprägsa- men Pfades erlaubt die Belegung des Quadrates durch einfaches Abzählen, eventuell unter Auslassung einer einzigen Zahl. Die so gefundene ... Read more

A method for pointwise evaluation of polyconvex envelopes

  • T. Bosse, L. Eneya, and A. Griewank
  • 2011
  • DOI: 10.1007/s13370-011-0035-9

We investigate a method for computing the value of a polyconvex envelope at a given feed A0∈Rm×n . The method generalizes an approach for computing convex envelopes proposed by Michelsen (Fluid Phase Equilibria 9:1–19, 1982; Fluid Phase Equilibria 9:21–40, 1982) and later implemented by McKinnon and Mongeau (J Glob Optim 12(4):325–351, 1998). We formulate the problem as a primal-dual nonlinear optimization task in p(1 + mn) variables (Λ,A)∈Rp×(Rm×n)p subject to ... Read more

On Hessian- and Jacobian-free SQP methods - a total quasi-Newton scheme with compact storage

  • T. Bosse, A. Griewank, and V. Schloßhauer
  • 2010
  • DOI: 10.1007/978-3-642-12598-0_6

In this paper we describe several modifications to reduce the memory requirement of the total quasi-Newton method proposed by Andreas Griewank et al. The idea is based on application of the compact representation formulae for the wellknown BFGS and SR1 update for unconstrained optimization. It is shown how these definitions can be extended to a total quasi-Newton approach for the constrained case. A brief introduction to the limited-memory approach is described in the present paper using ... Read more

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