Oberseminar

Oberseminar , Nummer im Vorlesungsverzeichnis: 10514

SWS: 2

Erste Veranstaltung am: 19.04.2010
Letzte Veranstaltung am: 19.07.2010

Dozenten

Lars Grüne, Klaus Schittkowski

Termine

  • Montag von 16:15 Uhr bis 17:45 Uhr, Raum S82 (NW II)

Allgemeines

Oberseminar von Prof. Dr. K. Chudej, Prof. Dr. L. Grüne, Prof. Dr. H. J. Pesch und Prof. Dr. K. Schittkowski

Vortragsankündigungen für das Oberseminar

Im Rahmen unseres gemeinsamen Oberseminars finden folgende Vorträge statt:  

Am Montag, dem 27. September 2010, um 14:15 Uhr im S 111, Gebäude AI, spricht

Herr Sven Leyffer
Mathematics and Computer Science (MCS) Division,

Argonne National Laboratory (ANL), Argonne, Illinois, USA



über das Thema
"Recent Advances in MINLP".


Abstract:

Many complex systems arising in scientific and engineering applications involve both discrete decisions and nonlinear system dynamics that affect the optimality of the final design. Mixed-integer nonlinear programming (MINLP) optimization problems combine the difficulty of optimizing over discrete variable sets with the challenges of handling nonlinear functions. MINLPs arise in a range of scientific and operational applications, including the operational reloading of nuclear reactors, the design of water distribution networks, the design and operation of electrical power systems, the integrated design and control of chemical processes, the design of wireless networks, and the minimization of the environmental impact of utility plants.
We present some novel MINLP applications, and review existing solution techniques.
We introduce a new package for solving mixed-integer nonlinear optimization problems, called MINOTAUR. MINOTAUR implements a range of branch-and-cut algorithms within a flexible object-oriented framework. We will comment on some software design issues and describe some recent work on tighter integrating nonlinear solvers into a branch-and-cut framework.

 


Am Montag, dem 02. August 2010, um 16:15 Uhr im S 82, Gebäude NW II, spricht

Herr Zaikun Zhang
Academy of Mathematics and Systems Science (AMSS)

Chinese Academy of Sciences, Beijing, China



über das Thema
"Derivative-Free Optimization Based on Interpolation".


Einladung: PDF-file

Abstract:

We consider derivative-free optimization problems, i.e., optimization problems defined by functions for which derivatives are unavailable. Powell's NEWUOA method and a modification are discussed. The methods are based on trust region technique and interpolation. In each iteration, a quadratic model Q is constructed by interpolating the objective function at m points, and is minimized in the trust region to generate a new point. It is introduced how to obtain Q when m < (n + 1)(n + 1)/2, where n is the dimension of the problem. Numerical results are given to show the behavior of our methods. 

 


Am Montag, dem 26. Juli 2010, um 16:15 Uhr im S 82, Gebäude NW II, spricht

Herr Dipl.-Math Martin Schlüter
Theoretical & Computational Optimization Group

School of Mathematics

University of Birmingham



über das Thema
"MIDACO – A new global optimizer for black-box MINLP".


Einladung: PDF-file

Abstract:

A new solver for general black-box MINLP is presented. It is based on an extended Ant Colony Optimization (ACO) metaheuristic and the recently introduced oracle penalty method. Along with a brief introduction in the theory of the proposed algorithm, specific features of the implementation and comprehensive numerical results are presented, which reveal the potential of this new approach.

Summary:

Recently the field of mixed integer nonlinear programming (MINLP) is gaining more and more popularity. While most approaches follow strict determinist algorithms, here a purely stochastic approach is introduced. In contrast to its deterministic counterparts it is able to treat the MINLP as black-box without the necessity of smooth or somewhat natural functions. On the other hand, it might require (due to its stochastic nature) much more function evaluations to reach a subsetcient solution quality.
The approach is based on a mixed integer extension of the Ant Colony optimization (ACO) algorithm using the recently introduced oracle penalty method to deal with equality and inequality constraints. An implementation, named MIDACO, is presented along with its basic features. Among those features are massive parallelization options along with gateways to Fortran, C/C++ and Matlab and a very user friendly setup.
Extensive numerical results are presented to verify the strength and practical usefulness of this new approach. Not only benchmark problems, but also several real world applications from chemical engineering and aerospace design are discussed and compared with concurrent optimization approaches. It will be demonstrated, that MIDACO is not only competitive with state of the art algorithms for non-convex NLP's and MINLP's, but often even outperforms those in terms of the solution quality and calculation time.
 

 


Am Montag, dem 19. Juli 2010, um 16:15 Uhr im S 82, Gebäude NW II, spricht

Herr Stud. rer. nat. Thomas Jahn
Lehrstuhl für Angewandte Mathematik
Universität Bayreuth


über das Thema
"Parallelizing the MPC concept on CUDA hardware".


Einladung: PDF-file

Abstract:

Model predictive control (MPC) is based on iterative solutions of optimal control problems. Naturally large-scaled control problems can cause higher numerical effort than small ones.
In this talk we analyze the possibility of reducing computing time of the numerical algorithms by massive parallelization. Especially modern graphic boards seem to be suitable due to numerous GPU processors. The main topic is the implementation of the algorithm on Nvidia's graphics hardware coming with a technology called “CUDA”, that enables programmers to directly take control of the GPU capabilities. It will be shown that some parameters of the MPC algorithm (e.g. horizon size) and the structure of the controlled system have to be in compliance with several requirements of the hardware in order to manage efficient execution of the algorithm.
The required properties of the system will be discussed during the task and it will be shown, that a centralized control of a swarm of objects fulfills all requirements. Numerical simulation of a swarm example will reveal the enormous reduction of computing time compared to a conventional CPU.
 

 


Am Montag, dem 12. Juli 2010, um 16:15 Uhr im S 82, Gebäude NW II, spricht

Herr Dipl.-Wirtschaftsmath. Karl Worthmann
Lehrstuhl für Angewandte Mathematik
Universität Bayreuth


über das Thema
"Stability Analysis of Receding Horizon Schemes without terminal constraints".


Einladung: PDF-file

Abstract:

In this talk we consider receding horizon control (RHC) – also termed model predictive control (MPC) – without terminal constraints. This technique relies on the iterative (online) solution of finite horizon optimal control problems in order to deal with an optimal control problem posed on an infinite time horizon. In contrast to the pre-dominant approach in the literature which incorporates additional (artificial) terminal constraints and/or costs in order to ensure stability of the MPC closed-loop we investigate the stability behaviour of unconstrained MPC schemes. Based on a controllability condition and Bellman's principle of optimality a linear program can be deduced whose solution coincides with a suboptimality index. A positive suboptimality index guarantees the validity of a relaxed Lyapunov inequality which allows for concluding asymptotic stability and performance bounds.
Moreover, we show that an additional growth condition which may, e.g., reflect continuity properties of the system in consideration can be incorporated. This leads to tighter estimates which characterize the stability behaviour of the MPC closed-loop more accurately. As a consequence, our stability analysis can also be applied to discrete time systems induced by sampled-data systems with very fast sampling which is often required in order to preserve stability properties.

 


Am Montag, dem 5. Juli 2010, um 16:15 Uhr im S 82, Gebäude NW II, spricht

Herr Dipl.-Math. Nils Altmüller
Lehrstuhl für Angewandte Mathematik
Universität Bayreuth


über das Thema
"Model predictive control of PDEs".


Einladung: PDF-file

Abstract:

Model predictive control (MPC) is a well established method for the control of dynamical systems. It is widely used in industrial applications.
In this talk we consider MPC of time dependent parabolic and hyperbolic PDEs. We present stability results for the linear wave equation and particularly we analyze the case of instantaneous control. Because real time PDE-constrained optimization is in general difficult we combine predictive control and model reduction techniques (Proper Orthogonal Decomposition). Numerical results for semilinear parabolic PDEs are presented.

 


Am Montag, dem 28. Juni 2010, um 16:15 Uhr im S 82, Gebäude NW II, spricht

Herr Dipl.-Wirtschaftsmath. Axel Luthardt 
EADS Military Air Systems – System Engineering – Operations Analysis


über das Thema
"A new trust-region algorithm with convex approximations".


Einladung: PDF-file

Abstract:

A new SCP-method for solving general continuous non-linear programs is introduced combining MMA-approximations with a trust-region strategy. The trust-region of this method is defined as the area between the asymptotes used for the MMA-approximations, minus a fixed safety distance due to boundedness of the derivations of the approximation. The asymptotes necessary for the approximation are generated implicit by controlling the trust-region in the sense of a trust-region method. A prove of global convergence of the new method is sketched and the algorithm Trust-Region Sequential Convex Programming TRSCP is presented. Hence TRSCP is the implementation of a SCP- as well as a trust- region method. Different to other approaches in this area, TRSCP did not need an explicit trust-region and asymptotes combination. Further more, an active trust-region causes no problem for convergence of the new method.

Am Montag, dem 14. Juni 2010, um 16:15 Uhr im S 82, Gebäude NW II, spricht

Frau Dipl.-Wirtschaftsmath. Sonja Lehmann
Angewandte Informatik VII - Kontinuierliche Optimierung, Fachgruppe Informatik,
Universität Bayreuth


über das Thema
"A feasible sequential convex programming method".


Einladung: PDF-file

Abstract:

In many real world optimization problems, model functions can only be evaluated on a special subset F of the feasible region which is described by additional nonlinear constraints. To ensure feasibility with respect to this subset, it is required that all iterates of an optimization algorithm retain strictly feasible while all the other constraints may be violated during the iteration process.
We propose a modification of a sequential convex programming (SCP) method which ensures that the solutions of all subproblems stay in the subset F. The general idea of SCP is to generate a sequence of strictly convex and separable subproblems, where an augmented Lagrangian merit function is applied to perform a line search and to guarantee convergence from arbitrary starting points. In our proposed modification, the resulting subproblems are expanded by additional constraints, describing F, to guarantee feasibility with respect to this subset in each iteration step. The algorithm is introduced and some numerical examples from Free Material Optimization are presented.
 

Am Montag, dem 14. Juni 2010, um 16:15 Uhr im S 82, Gebäude NW II, spricht

Herr Dipl.-Math. Björn Sachsenberg
Angewandte Informatik VII - Kontinuierliche Optimierung, Fachgruppe Informatik,
Universität Bayreuth.

über das Thema
"Mixed-Integer Nonlinear Programming based on Mixed-Integer Quadratic Approximations".
 

 

Einladung: PDF-file

Abstract:

We propose a numerical algorithm for solving large scale smooth nonlinear programming problems. The algorithm is based on an SQP method where the quadratic subproblem is solved by a primal-dual interior point method. A feature of the algorithm is, that the quadratic subproblem is not necessarily solved exactly. Theoretical details and some numerical results are presented.



Am Montag, dem 07. Juni 2010, um 16:15 Uhr im S 82, Gebäude NW II, spricht

Herr Dipl.-Wirtschaftsmath. Thomas Lehmann
Angewandte Informatik VII - Kontinuierliche Optimierung, Fachgruppe Informatik,
Universität Bayreuth


über das Thema
"Mixed-Integer Nonlinear Programming based on Mixed-Integer Quadratic Approximations".


Am Montag, dem 31. Mai 2010, um 16:15 Uhr im S 82, Gebäude NW II, spricht

Herr Dipl.-Wirtschaftsmath. Oliver Exler
Angewandte Informatik VII - Kontinuierliche Optimierung, Fachgruppe Informatik,
Universität Bayreuth


über das Thema
"A Trust Region SQP method without second order correction for solving constrained nonlinear optimization problems".


Einladung: PDF-file

Abstract:

A sequential quadratic programming (SQP) method for constrained nonlinear optimization problems is presented. Global convergence of the approach is guaranteed by using trust region techniques. In order to guarantee local convergence with a superlinear rate the Augmented Lagrangian penalty function is used as a merit function. Applying this merit function avoids the necessity of calculating second order correction steps, i.e. solving additional quadratic subproblems. Theoretical details are presented. Additionally, numerical results are shown that verify the efficiency of the proposed method.


Am Montag, dem 10. Mai 2010, um 16:15 Uhr im S 82, Gebäude NW II, spricht

Herr Prof. Dr. Sergey Dashkovskiy
AG Technomathematik, Zentrum für Technomathematik,
Fachbereich 3 - Mathematik, Universität Bremen
z.Zt. Universität Bayreuth


über das Thema
"Stabilität gekoppelter nichtlinearer Systeme".


Einladung: PDF-file

Abstract:

Im Rahmen der Eingang-Zustand-Stabilität (Englisch: input-to-state stability, ISS) untersuchen wir, ob diese Eigenschaft erhalten bleibt, wenn man mehrere Systeme miteinander verbindet. Wir betrachten Stabilitätsbedingungen unter welchen die ISS-Eigenschaft erhalten bleibt und zeigen, wie man eine ISS-Lyapunov-Funktion in diesem Fall konstruieren kann.


Einladende:

Prof. Dr. Kurt Chudej
Prof. Dr. Lars Grüne
Prof. Dr. Hans Josef Pesch
Prof. Dr. K. Schittkowski

Lehrstuhl -

|  Universität Bayreuth -