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Chair of Applied Mathematics
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(MATHE V)
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Oberseminar in SS 2010
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Vortragsankündigungen für das Oberseminar
Im Rahmen unseres gemeinsamen Oberseminars
finden folgende Vorträge
im S 82
statt:
Am
Montag, dem 27. September 2010, um 14:15 Uhr im
S 111, Gebäude AI, spricht
über das Thema
| "Recent Advances in MINLP".
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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
über das Thema
| "Derivative-Free Optimization Based on Interpolation".
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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
über das Thema
| "MIDACO – A new global optimizer for black-box MINLP".
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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
über das Thema
| "Parallelizing the MPC concept on CUDA hardware".
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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
über das Thema
| "Stability Analysis of Receding Horizon Schemes
without terminal constraints".
|
Einladung (PDF-file)
Summary:
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 05. Juli 2010, um 16:15 Uhr im
S 82, Gebäude NW II, spricht
über das Thema
| "Model predictive control of PDEs".
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Einladung (PDF-file)
Summary:
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
über das Thema
| "A new trust-region algorithm with convex approximations".
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Einladung (PDF-file)
Summary:
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 21. Juni 2010, um 16:15 Uhr im
S 82, Gebäude NW II, spricht
über das Thema
| "A feasible sequential convex programming
method".
|
Einladung (PDF-file)
Zusammenfassung:
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
über das Thema
| "An SQP Interior Point algorithm for solving large
scale nonlinear optimization problems".
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Einladung (PDF-file)
Zusammenfassung:
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
über das Thema
| "Mixed-Integer Nonlinear Programming based on
Mixed-Integer Quadratic Approximations".
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Am
Montag, dem 31. Mai 2010, um 16:15 Uhr im
S 82, Gebäude NW II, spricht
über das Thema
| "A Trust Region SQP method without second order correction
for solving constrained nonlinear optimization problems".
|
Einladung (PDF-file)
Zusammenfassung:
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
über das Thema
| "Stabilität gekoppelter nichtlinearer Systeme".
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Einladung (PDF-file)
Zusammenfassung:
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:
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Last modified: $Date: 2011/04/27 17:53:24 $
Chair of Appl. Math.