Prof. Klaus Schittkowski
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Development of a Large-Scale Nonlinear Programming Code for Structural Mechanical Optimization

funding: MAAXIMUS (subcontractor)
cooperation: EADS, Munich
period: 1.4.2008 - 30.9.2010 
researcher:  B. Sachsenberg

For solving large-scale optimization programs, an SQP-based interior-point 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 FE-system Lagrange developed by EADS. The goal is to solve very large mechanical structural design optimization problems.

Development of a Toolbox for Mixed-Integer Nonlinear Programming

funding: Shell GameChanger
cooperation: Shell Rijswijk
period: 1.1.2007 - 31.12.2009 
researcher:  T. Lehmann

Goal of the project is the development of algorithms and a program library  (toolbox) for solving mixed-integer 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 second-order 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 mixed-integer 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 (branch-and-cut).

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 multi-class separation.

Development of Large Scale SCP-Methods for Free Material Optimization

funding: EU Specific Targeted Research Program (6th Framework Program Aeronautics and Space) PLATO-n, A PLAtform for Topology Optimisation incorporating Novel, Large-Scale, 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 line-search sub-algorithms or of trust regions in combination with the moving asymptotes. Moreover, active-set 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

Computer-aided 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 piezo-acoustic 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 time-consuming and derivatives must be approximated by forward differences. Thus, the sequential quadratic programming (SQP) code NLPQL is extended to handle additional integer variables.

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