Birla Institute of Technology & Science, Pilani  Hyderabad
Optimization
AA 2222

Spring 2013
Introduction
Goal: Learn inputoutput systems: given an input, predict output.
Gaussian Process Regression (GPR): powerful nonparametric regression
technique
Kriging and spline ts are both instances of GPR
Outline for today:
Gaussian random vectors, m
Birla Institute of Technology & Science, Pilani  Hyderabad
Optimization
AA 2222

Spring 2013
An Introduction to the Conjugate Gradient Method Without the Agonizing Pain
Edition 1 1 4 Jonathan Richard Shewchuk August 4, 1994
School of Computer Science Carnegie Mellon University Pittsburgh, PA 15213
Abstract
The Conjugate Gradient Method is the mos
Birla Institute of Technology & Science, Pilani  Hyderabad
Optimization
AA 2222

Spring 2013
AIAA JOURNAL
Vol. 38, No. 8, August 2000
Bilevel Integrated System Synthesis with Response Surfaces
Srinivas Kodiyalam
Lockheed Martin Space Systems Company, Sunnyvale, California 94089
and
Jaroslaw SobieszczanskiSobieski
NASA Langley Research Center, Ha
Birla Institute of Technology & Science, Pilani  Hyderabad
Optimization
AA 2222

Spring 2013
The Conjugate Gradient Method
Jason E. Hicken
Aerospace Design Lab
Department of Aeronautics & Astronautics
Stanford University
14 July 2011
Lecture Objectives
describe when CG can be used to solve Ax = b
relate CG to the method of conjugate directions
de
Birla Institute of Technology & Science, Pilani  Hyderabad
Optimization
AA 2222

Spring 2013
AA222: MDO
5
Sunday 1st April, 2012 at 19:48
About This Course
Course Administrative Information
Instructors: Dr. Jason E. Hicken1 and Prof. Juan J. Alonso2
Course Assistant: TBA
Oce Hours: J. Hicken: Fridays 2:003:30pm (Prof. Alonso: TBA)
Schedule:
Birla Institute of Technology & Science, Pilani  Hyderabad
Optimization
AA 2222

Spring 2013
AA222: MDO
Friday 6th April, 2012 at 12:06
53
Chapter 3
GradientBased Optimization
3.1
Introduction
In Chapter 2 we described methods to minimize (or at least decrease) a function of one variable.
While problems with one variable do exist in MDO, most pr
Birla Institute of Technology & Science, Pilani  Hyderabad
Optimization
AA 2222

Spring 2013
AIAA JOURNAL
Vol. 41, No. 10, October 2003
Bilevel Integrated System Synthesis for Concurrent
and Distributed Processing
Jaroslaw SobieszczanskiSobieski
NASA Langley Research Center, Hampton, Virginia 23681
and
Troy D. Altus, Matthew Phillips, and Robert
Birla Institute of Technology & Science, Pilani  Hyderabad
Optimization
AA 2222

Spring 2013
Thursday 26th April, 2012 at 16:05
113
AA222: MDO
Chapter 5
Constrained Optimization
Engineering design optimization problems are very rarely unconstrained. Moreover, the constraints
that appear in these problems are typically nonlinear. This motivates ou
Birla Institute of Technology & Science, Pilani  Hyderabad
Optimization
AA 2222

Spring 2013
162
AA222: MDO
Friday 11th May, 2012 at 14:00
Chapter 7
Multidisciplinary Design Optimization
7.1
Introduction
Multidisciplinary design optimization (MDO) is a eld of engineering that focuses on use of numerical optimization to perform the design of syste
Birla Institute of Technology & Science, Pilani  Hyderabad
Optimization
AA 2222

Spring 2013
Regression Tutorial
Dev Rajnarayan
6 May, 2010.
1
Introduction
The topic of regression deals with continuous inputoutput systems, and the goal is to learn a given
system. Learning is measured by the ability to predict the output of the system to any give
Birla Institute of Technology & Science, Pilani  Hyderabad
Optimization
AA 2222

Spring 2013
1
1.1
GradientBased Optimization
General Algorithm for Smooth Functions
All algorithms for unconstrained gradientbased optimization can be described as follows. We
start with iteration number k = 0 and a starting point, xk .
1. Test for convergence. If
Birla Institute of Technology & Science, Pilani  Hyderabad
Optimization
AA 2222

Spring 2013
2
2.1
Single Variable Minimization and Line Searches
Motivation
Consider a scalar function, f , that depends on a single independent variable, x. Suppose we
want to nd the value of x where f (x) is a minimum value. Furthermore, we want to do with,
Low co
Birla Institute of Technology & Science, Pilani  Hyderabad
Optimization
AA 2222

Spring 2013
Monday 30th April, 2012 at 16:25
133
AA222: MDO
Chapter 6
GradientFree Optimization
6.1
Introduction
Using optimization in the solution of practical applications we often encounter one or more of the
following challenges:
nondierentiable functions and/
Birla Institute of Technology & Science, Pilani  Hyderabad
Optimization
AA 2222

Spring 2013
5
Handling Constraints
Engineering design optimization problems are very rarely unconstrained.
Moreover, the constraints that appear in these problems are typically nonlinear.
This motivates our interest in general nonlinearly constrained optimization
the
Birla Institute of Technology & Science, Pilani  Hyderabad
Optimization
AA 2222

Spring 2013
Friday 6th April, 2012 at 12:06
77
AA222: MDO
Chapter 4
Sensitivity Analysis
4.1
Introduction
Sensitivity analysis consists in computing derivatives of one or more quantities (outputs) with respect to one or several independent variables (inputs). Althoug
Birla Institute of Technology & Science, Pilani  Hyderabad
Optimization
AA 2222

Spring 2013
AA222: Sensitivity Analysis
AA222
Lecture 4
April 18, 2010
AA222: Introduction to Multidisciplinary Design Optimization
1
4
4.1
Sensitivity Analysis
Introduction
Sensitivity analysis consists in computing derivatives of one or more quantities (outputs) wi
Birla Institute of Technology & Science, Pilani  Hyderabad
Optimization
AA 2222

Spring 2013
Approximation Methods in Optimization
The basic idea is that if you have a function that is noisy and possibly
expensive to evaluate, then that function can be sampled at a few points
and a t of it created. Optimization is then performed not on the origi
Birla Institute of Technology & Science, Pilani  Hyderabad
Optimization
AA 2222

Spring 2013
Course for Winter 2011: AE 7141 Special Topics
Multidisciplinary Design Optimization Optimization
AA222: Introduction to Multidisciplinary Design
Joaquim R. R. A. Martins
http:/mdolab.engin.umich.edu/index.php/martins
Tuesdays and Thursdays at 1:303:00p
Birla Institute of Technology & Science, Pilani  Hyderabad
Optimization
AA 2222

Spring 2013
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Birla Institute of Technology & Science, Pilani  Hyderabad
Optimization
AA 2222

Spring 2013
1
Introduction
Multidisciplinary design optimization (MDO): a eld of engineering that
uses numerical optimization to perform the design of systems that involve a
number of disciplines or subsystems.
the best design of a multidisciplinary system can only
Birla Institute of Technology & Science, Pilani  Hyderabad
Optimization
AA 2222

Spring 2013
Information Diusion on the Iterated Local Transitivity
Model of Online Social Networks
Lucy Smalla,1 , Oliver Masona,1,
a Hamilton
Institute, National University of Ireland Maynooth
Maynooth, Co. Kildare, Ireland
Abstract
We study a recently introduced de
Birla Institute of Technology & Science, Pilani  Hyderabad
Optimization
AA 2222

Spring 2013
Graph Theory and Networks in Biology
Oliver Mason and Mark Verwoerd
Hamilton Institute, National University of Ireland
Maynooth, Co. Kildare, Ireland
cfw_oliver.mason, [email protected]
January 17, 2007
Abstract
In this paper, we present a survey of t
Birla Institute of Technology & Science, Pilani  Hyderabad
Optimization
AA 2222

Spring 2013
A version of this article appeared in Linear Algebra and its Applications,
Volume 438, Issue 7, 1 April 2013, Pages 29112928
DOI Information: http:/dx.doi.org/10.1016/j.laa.2012.11.020
1
The Analytic Hierarchy Process, Max Algebra and
Multiobjective Opti
Birla Institute of Technology & Science, Pilani  Hyderabad
Optimization
AA 2222

Spring 2013
On the KamkeMller conditions, monotonicity and
u
continuity for bimodal piecewisesmooth systems
Yoann ODonoghuea,1 , Oliver Masona,1, Rick Middletona,1
a Hamilton
Institute, National University of Ireland, Maynooth
Maynooth, Co. Kildare, Ireland
Abstra
Birla Institute of Technology & Science, Pilani  Hyderabad
Optimization
AA 2222

Spring 2013
Electronic Journal of Linear Algebra ISSN 10813810
A publication of the International Linear Algebra Society
Volume 26, pp. 1527, January 2013
ELA
http:/math.technion.ac.il/iic/ela
ON THE MARKOV CHAIN TREE THEOREM
IN THE MAX ALGEBRA
BUKET BENEK GURSOY ,
Birla Institute of Technology & Science, Pilani  Hyderabad
Optimization
AA 2222

Spring 2013
Diagonal Riccati Stability and Positive TimeDelay
Systems
Oliver Masona,1,
a Hamilton
Institute, National University of Ireland, Maynooth
Maynooth, Co. Kildare, Ireland
Abstract
We consider a class of algebraic Riccati equations arising in the study of p