# Csls workshop on optimization of eigenvalues

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## Workshop overview

A wealth of interesting problems in engineering, control, finance, and statistics can be formulated as optimization problems involving theeigenvalues of a matrix function. These very challenging problems cannot usually be solved via traditional techniques for nonlinearoptimization. However, they have been addressed in recent years by a combination of deep, elegant mathematical analysis and ingeniousalgorithmic and software development. In this workshop, three leading experts will discuss applications along with the theoretical andalgorithmic aspects of this fascinating topic.

Remark: This workshop was held on October 7, 2004 as part of the Computational Sciences Lecture Series (CSLS) at the University of Wisconsin-Madison.

## Semidefinite programming

By Prof. Stephen Boyd (Stanford University, USA)

Slides of talk [PDF] (Not yet available.) | Video [WMV] (Not yet available.)

ABSTRACT: In semidefinite programming (SDP) a linear function is minimized subject to the constraint that the eigenvalues of asymmetric matrix are nonnegative. While such problems were studied in a few papers in the 1970s, the relatively recent development ofefficient interior-point algorithms for SDP has spurred research in a wide variety of application fields, including control system analysisand synthesis, combinatorial optimization, circuit design, structural optimization, finance, and statistics. In this overview talk I willcover the basic properties of SDP, survey some applications, and give a brief description of interior-point methods for their solution.

## Eigenvalue optimization: symmetric versus nonsymmetric matrices

By Prof. Adrian Lewis (Cornell University, USA)

Slides of talk [PDF] (Not yet available.) | Video [WMV] (Not yet available.)

ABSTRACT: The eigenvalues of a symmetric matrix are Lipschitzfunctions with elegant convexity properties, amenable to efficient interior-point optimization algorithms. By contrast, for example, thespectral radius of a nonsymmetric matrix is neither a convex function, nor Lipschitz. It may indicate practical behaviour much less reliablythan in the symmetric case, and is more challenging for numerical optimization (see Overton's talk). Nonetheless, this function doesshare several significant variational-analytic properties with its symmetric counterpart. I will outline these analogies, discuss thefundamental idea of Clarke regularity, highlight its usefulness in nonsmooth chain rules, and discuss robust regularizations of functionslike the spectral radius. (Including joint work with James Burke and Michael Overton.)

## Local optimization of stability functions in theory and practice

By Prof. Michael Overton (Courant Institute of Mathematical Sciences New York University,USA)

Slides of talk [PDF] (Not yet available.) | Video [WMV] (Not yet available.)

ABSTRACT: Stability measures arising in systems and control are typically nonsmooth, nonconvex functions. The simplest examples arethe abscissa and radius maps for polynomials (maximum real part, or modulus, of the roots) and the analagous matrix measures, the spectralabscissa and radius (maximum real part, or modulus, of the eigenvalues). More robust measures include the distance to instability(smallest perturbation that makes a polynomial or matrix unstable) and the $\epsilon$ pseudospectral abscissa or radius of a matrix (maximumreal part or modulus of the $\epsilon$\-pseudospectrum). When polynomials or matrices depend on parameters it is natural to consideroptimization of such functions. We discuss an algorithm for locally optimizing such nonsmooth, nonconvex functions over parameter spaceand illustrate its effectiveness, computing, for example, locally optimal low-order controllers for challenging problems from theliterature. We also give an overview of variational analysis of stabiity functionsin polynomial and matrix space, expanding on some of the issues discussed in Lewis's talk. (Joint work with James V. Burke and AdrianS. Lewis.)

where we get a research paper on Nano chemistry....?
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
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