Projects
EADS MINLP
SVM
SCP PASCAL
EPCOS

Development of a LargeScale Nonlinear Programming Code
for Structural Mechanical Optimization
funding: 
MAAXIMUS
(subcontractor) 
cooperation: 
EADS,
Munich 
period: 
1.4.2008  30.9.2010 
researcher: 
B. Sachsenberg 
summary: 
For solving
largescale optimization programs, an SQPbased interiorpoint
method is to be developed. Hessian updates are performed by the limited
memory BFGS method. Very large systems of linear equations are solved by
direct and indirect solvers with external data organization. The code is
to be integrated into the FEsystem Lagrange developed by EADS. The goal
is to solve very large mechanical structural design optimization
problems.



Development of a Toolbox
for MixedInteger Nonlinear Programming
funding: 
Shell
GameChanger 
cooperation: 
Shell Rijswijk 
period: 
1.1.2007  31.12.2009 
researcher: 
T. Lehmann 
summary: 
Goal of the project
is the development of algorithms and a program library (toolbox)
for solving mixedinteger nonlinear optimization problems. The toolbox
is to be integrated into existing simulation software of the SHELL and
to be tested on practically relevant examples.
An SQP algorithm is developed based on trust regions with secondorder corrections. Convergence properties of the SQP algorithm are to be analyzed,
especially the approximation of derivatives subject to integer variables
at grid points. To avoid excessive calculation times for solving mixedinteger
quadratic programming subproblems, more efficient
methods are to be investigated and implemented, for example by applying
early branching by exploiting dual information, or cutting plane
techniques known from linear programming (branchandcut).
The toolbox is to be tested on academic examples and to be
integrated into available simulation software of the SHELL at his
institution. Examples are Shell’s Modular Reservoir Simulator (MoReS),
Hydrocarbon Field Planning Tool (HFPT), Production Universe (PU),
Production and Revenue Optimizer (PRO), and further production control
software.



Interior Point Methods for
Parameter Selection of Support Vector Machines
funding: 
International Doctorate Program (IDK) within the Elite
Network of Bavaria (ENB) Identification, Optimization and Control
with Applications in Modern Technologies 
period: 
1.1.2006  30.9.2009 
researcher: 
T. Spickenreuther

summary: 
We consider bilevel optimization problems
with a convex quadratic program at the lower lever. The problem is
transformed into a mathematical program with complementary constraints (MPCC),
which is then solved by an interior point method.
The resulting algorithm is to be applied to minimize a test error over
solutions of a support vector machines (SVM) subject to a given set of
training data. The idea is to adopt unknown SVM parameters
automatically, i.e., without applying costly statistical search methods
like cross validation. A particular advantage is that also problems with
a larger number of parameters can be solved, for example for feature
selection and multiclass separation.



Development of Large Scale SCPMethods for Free Material Optimization
funding: 
EU Specific Targeted Research Program
(6th Framework Program Aeronautics and Space)
PLATOn,
A PLAtform for Topology
Optimisation incorporating Novel, LargeScale, Free
Material Optimisation and Mixed Integer Programming Methods 
period: 
1.10.2006  31.12.2009 
researcher: 
S. Ertel 
summary: 
For solving very large scale topology optimization
problems (FMO),
a
general optimization frame is to be developed following the sequential
convex programming (SCP) scheme. Special stabilization techniques are
introduced in form of linesearch subalgorithms or of trust regions in
combination with the moving asymptotes. Moreover, activeset strategies
for a large number of constraints and efficient solvers for convex
subproblems and sparse linear systems of equations will be provided.
New types of constraints are to be considered, e.g., stress and buckling
constraints, for which analytical derivatives are derived. The resulting
code is integrated under a common platform in strong cooperation with
partner institutes.



Support
Vector Machines for Machine Learning
funding: 
EU Network of Excellence
PASCAL (Pattern
Analysis, Statistical Modeling, and Computational Learning) 
period: 
1.1.2004  31.12.2008 
researcher: 
diploma students 
summary: 
We investigate the question, whether and
how parameters of SVM kernels can be adopted automatically by
formulating and solving a nonlinear programming problem. Special
emphasis is given on a computational procedure for computing analytical
gradients of the solution of an SVM subject to kernel parameters.
Preliminary numerical results are obtained based on a set of 20 test
examples.



Optimal
Design of Electronic Components
sponsor: 
EPCOS
AG, München 
period: 
since 1.1.2000  31.10.2011 
researcher: 
diploma students 
summary: 
Computeraided design optimization of
electronic components is a powerful tool to reduce development costs on the one hand and to improve the performance of
bandpass filters on the other.
The physical model is based on the wave equations and the piezoacoustic effect.
A mathematical model of an electronic filter depends on certain geometry parameters such as length, height, number of metallized layers, etc.,
i.e., on continuous variables as well as on integer variables. Proceeding from the design goals of a customer, these geometric parameters of a filter are computed by maximizing
the transmission within a given interior frequency range under additional lower bounds for frequencies in certain outer
frequency ranges.
However, the mathematical model depends in addition on a couple of integer variables, for example the number of fingers,
leading to a more complex mixed integer nonlinear programming problem. One evaluation of the simulation code is extremely timeconsuming and derivatives must be approximated
by forward differences. Thus, the sequential quadratic programming (SQP) code
NLPQL
is extended to handle additional integer variables. 

