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Winter 2003
IMA Tutorial
Optimization in Simulation-Based Models
January 8, 2003

Optimization, September 2002 - June 2003

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.

(Including Tutorial Slides)

WEDNESDAY, JANUARY 8 All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
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.


As of 1/9/2003
Name Department Affiliation
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