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This tutorial provides an overview of the emerging area of simulation-based optimization. The unifying theme is the need to optimize systems governed by differential equations or other complex simulations. Optimal control, parameter identification, optimal design and inverse problems give rise to simulation-based optimization problems.
As the capabilities of both optimization and differential equations solvers increase, there is a growing interest in industry and science to optimize the performance of systems described by complex simulations. Solving these optimization problems poses a major challenge since it requires multiple solutions of the simulation problem -- a task that is by itself complex, delicate and computationally intensive. To be successful the optimization process must tightly coupled to the requirements of the simulation. The tutorial will present some of the most important applications of simulation-based optimization, will addess the challenges they pose to optimization technology, and will review some of the recent advances that have been made in this area.
TUTORIAL SCHEDULE
(Including
Tutorial Slides)
WEDNESDAY, JANUARY 8 All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted. | ||
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8:30-9:00 am | Coffee | Reception Room EE/CS 3-176 |
9:00-10:00 am |
Omar Ghattas Carnegie Mellon University |
Overview of simulation based optimization |
10:00-11:00 am |
Jorge Nocedal Northwestern University |
Challenges for optimization |
2:00-3:00 pm |
William W. Symes Rice University |
The reflection seismic inverse problem: a case study in simulation driven optimization Slides: pdf |
3:00-4:00 pm | Lorenz T. Biegler Carnegie Mellon University |
Optimization of ODE/DAE constrained models Slides: pdf |
Lorenz T. Biegler (Department of Chemical Engineering, Carnegie Mellon University) lb01+@andrew.cmu.edu http://www.cheme.cmu.edu/who/faculty/biegler.html
Optimization of ODE/DAE constrained models Slides: pdf
This talk will explore the structure of nonlinear programs that arise from ODE/DAE constrained optimization problems. Common optimization strategies for solving these problems will be reviewed. In particular, we will explore concepts of index and stability that have a strong impact on the regularity and conditioning of discretized problems. Also, a discussion of suitable NLP algorithms is presented for these problems along with examples that demonstrate their performance.
Omar Ghattas (Professor & Director Mechanics, Algorithms, & Computing Lab, Dept of Civil & Environmental Engineering, Dept of Biomedical & Health Engineering, Carnegie Mellon University) oghattas@cs.cmu.edu http://www.cs.cmu.edu/~oghattas
Overview of simulation based optimization
In this talk we will discuss problem formulation and will give examples of optimal design, control and inverse problems. We will consider the relationship between the infinite and finite-dimensional problem and some discretization issues (from the variational point of view). We will also discuss direct vs. adjoint sensitivities. The focus of this talk is on systems governed by partial differential equations, but it will also set the stage for the other talks in the tutorial.
Jorge Nocedal (ECE Department, Northwestern University) nocedal@ece.nwu.edu http://www.ece.nwu.edu/~nocedal
Challenges for optimization
Simulation-based optimization problems cannot be tackled (in general) with off-the shelf optimization software. In fact, most of the popular constrained optimization algorithms are not suitable for these types of applications and new algorithmic frameworks must be explored. In this talk we will describe the properties that optimization methods must possess so that they can be successfully integrated in simulation packages. All the important classes of constrained optimization algorithms will be analyzed, and possible extensions will be presented.
William W. Symes (Department of Computational and Applied Mathematics, Rice University) symes@caam.rice.edu
The reflection seismic inverse problem: a case study in simulation driven optimization Slides: pdf
Reflection seismology generates huge amounts of data encoding features of the Earth's subsurface, for example those that suggest the location of hydrocarbon deposits. The inverse problem of reflection seismology is to extract the Earth structure from this data. A variety of wave propagation theories predict seismic motion at varying levels of physical detail. Thus it is attractive to formulate the inverse problem as a simulation driven optimization problem.This tutorial will review the by-now standard steps in implementing an optimization approach to an inverse problem in PDE, shared with data assimilation, optimal design, and control problems. Fundamental features of wave propagation then make a rude entrance, producing highly multimodal objectives and so derailing what might have seemed the natural approach to this class of problems. Ideas from the applied geophysics literature suggest various other approaches, which yield much better behaved objectives. Similar behaviour might be expected in any control problem in which the state exhibits sharp or rapidly oscillating features whose location depends strongly on the control.
Name | Department | Affiliation |
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Natalia Alexandrov | Langley Research Center | NASA |
Oleg Alexandrov | Mathematics | University of Minnesota |
Montaz Ali | Computational And Applied Mathematics | Witwatersrand University |
Yusuf Bilgin Altundas | Schlumberger-Doll Research | |
Lorenz T. Biegler | Chemical Engineering | Carnegie Mellon University |
Daniel Boley | Computer Science | University of Minnesota |
Olga Brezhneva | Institute for Mathematics and its Applications | University of Minnesota |
Dongwei Cao | Computer Science | University of Minnesota |
Jamylle Carter | Mathematics | University of Minnesota |
Collette Coullard | Industrial Eng. & Mgmt. Sciences | Northwestern University |
Bob M. Crone | Mechanical R&D | Seagate Technology |
Prodromos Daoutidis | Chemical Engineering &Materials Sci. | University of Minnesota |
John Dennis | Computational & Applied Mathematics | Rice University |
Gregory S. Duane | University of Minnesota | Institute for Mathematics and its Applications |
Grant Erdmann | Mathematics | University of Minnesota |
Omar Ghattas | Civil and Environmental Engineering | Carnegie Mellon University |
Balaji Gopalakrishnan | Institute for Mathematics and its Application | University of Minnesota |
Genetha Anne Gray | Computational Sciences & Mathematics | Sandia National Laboratories |
Robert Gulliver | Mathematics | University of Minnesota |
Daniel Kerm | University of Minnesota | Institute for Mathematics and its Applications |
Tamara Gibson Kolda | Sandia National Laboratories | |
James Allan Lavrenz | Scientific Computation | University of Minnesota |
Guang-Tsai Lei | Mayo Clinic | |
Robert Michael Lewis | Mathematics | The College of William & Mary |
Wade Martinson | Process Solutions Technology Development Center | Cargill, Inc. |
Aurelia Minut | University of Minnesota | Institute for Mathematics and its Applications |
Hans Mittelmann | Mathematics | Arizona State University |
Thanasak Mouktonglang | Mathematics | University of Notre Dame |
Jorge Nocedal | Electrical & Computer Engineering Department | Northwestern University |
Jeong-Soo Park | Statistics | Chonnam National University, Korea |
Samuel Patterson | Mathematics and Computer Science | Carleton College |
Fay Salmon | SEMS Corporate Tecnology Center | 3M |
M. Nuri Sendil | Industrial Eng. & Mgmt. Sciences | Northwestern University |
William W. Symes | Dept. of Computational & Applied Mathematics | Rice University |
Olga Brezhneva | Institute for Mathematics and its Applications | University of Minnesota |
Cristina U. Thomas | OMTC | 3M |
Virginia Torczon | Computer Science | The College of William & Mary |
Luis Nunes Vicente | Matematica | Universidade de Coimbra, Portugal |
Amy R. Wilson | Health Services Research and Policy | University of Minnesota |
Dexuan Xie | Mathematical Sciences | University of Wisconsin-Milwaukee |
Man-Chung Yeung | Mathematics | University of Wyoming |
Tianyu Zhang | Mathematics | University of Minnesota |
Jun Zhao | Schlumberger-Doll Research |