Miguel Anjos

Miguel F. Anjos is a Lecturer (Assistant Professor) in the Faculty of
Mathematical Studies of the University of Southampton. He received his Ph.D.
in 2001 from the University of Waterloo, Canada, working under the
supervision of Professor Henry Wolkowicz. He previously completed a B.Sc.
with First Class Honours in Computer Science at McGill University, and an
M.S. in Scientific Computing and Computational Mathematics at Stanford
University. More recently, he held a postdoctoral research fellowship at the
Institute for Computer Science of the University of Cologne.
His research interests lie in in the application of continuous optimization
techniques, primarily convex optimization, to NPhard combinatorial
optimization problems.

Title of the talk:
An Improved Semidefinite Programming Relaxation for Satisfiability
(SAT)
Abstract:
The satisfiability (SAT) problem is a central problem in mathematical logic,
computing theory, and artificial intelligence. An instance of SAT is
specified by a set of boolean variables and a propositional formula in
conjunctive normal form. Given such an instance, the SAT problem asks
whether there is a truth assignment to the variables such that the formula
is satisfied. It is well known that SAT is in general NPcomplete, although
several important special cases can be solved in polynomial time. We are
interested in the application of SDP to satisfiability problems, and in
particular in how SDP can be used to detect unsatisfiability.
In this talk we introduce a new SDP relaxation for the satisfiability
problem. To derive this SDP relaxation, we first formulate SAT as an
optimization problem involving matrices. This formulation yields an SDP
relaxation which significantly improves on the previous relaxation in the
literature. The improved SDP relaxation arises from the recently introduced
paradigm of ``higher liftings'' for constructing semidefinite programming
relaxations of discrete optimization problems. The important characteristics
of the SDP relaxation are its ability to prove that a given SAT formula is
unsatisfiable independently of the lengths of the clauses in the formula,
its potential to yield truth assignments satisfying the SAT instance if a
feasible matrix of sufficiently low rank is computed, and the fact that it
is more amenable to practical computation than previous SDPs arising from
higher liftings. We present theoretical and computational results that
support these claims.

Etienne de Klerk

Etienne de Klerk is an assistant professor at the Faculty of Information
Technology and Systems of the
Delft University of Technology in the Netherlands.
Research interests: Conic optimization, approximation algorithms for global
and combinatorial optimization, interior point algorithms.
Current teaching: Nonlinear programming, Combinatorial Optimization,
Randomized Algorithms

Title of the talk:
Solving standard quadratic optimization problems
via copositive programming.
Coauthor: I.M. Bomze (University of Vienna).
Abstract:
The problem of minimizing a (nonconvex) quadratic function over
the simplex (the standard quadratic optimization problem)
has an exact convex reformulation as a copositive
programming problem. In this talk we show how to approximate the
optimal solution by approximating the cone of copositive matrices
via systems of linear inequalities, and, more refined, linear
matrix inequalities (LMI's).
In particular, we show that our approach leads to a
polynomialtime approximation scheme for the standard quadratic
optimization problem. This is an improvement on the previous
complexity result by Nesterov who showed
that a 2/3approximation is always possible.

Michal Kocvara

Michal Kocvara is currently with the Institute of Applied Mathematics,
University of Erlangen, Germany, on leave from the Institute of
Information Theory and Automation, Academy of Sciences of the Czech
Republic, Prague. In 1991 he obtained his CSc. (Ph.D.) degree in
Mathematics at the Mathematical Institute of the Czechoslovak Academy
of Sciences, and in 2001 he obtained his DrSc. habilitation in
Mathematics at the Charles University in Prague.
His research interests include structural optimization (material
optimization of linear elastic bodies;
truss optimization including single and multiple load topo or
geo/topo design with displacement, stability and robustness constraints;
shape optimizations of elastic bodies governed by variational
inequalities), algorithms for the solution of large and sparse
mathematical programs arising in structural optimization problems
(these include PENNON, a code for convex and nonconvex problems of
Nonlinear and Semidefinite Programming, and an iterative method for
linear complementarity problems), and
mathematical programs with equilibrium constraints (MPEC).

Title of the talk:
PENNON  A Generalized Augmented Lagrangian Method
for Semidefinite Programming.
Coauthor: Michael Stingl (University of ErlangenNürnberg).
Abstract: We describe a generalization of the PBM method by BenTal and
Zibulevsky to convex semidefinite programming problems. The algorithm
used is a generalized version of the Augmented Lagrangian method.
We present details of this algorithm as implemented in the code PENNON.
The code can also solve secondorder conic programming (SOCP) problems,
as well as problems with a mixture of SDP, SOCP and NLP constraints.
Results of extensive numerical tests and comparison with other SDP codes
are presented.

Monique Laurent

Monique Laurent received her Ph.D. at the University of Paris VII in 1986.
After two years of employment as a research engineer at
CNET (Centre National d'Etudes des Télécommunications),
she became a researcher at CNRS (Centre National de la Recherche
Scientifique). She joined first the University Paris Dauphine and,
from 1992, she was a member of the computer science departement
at Ecole Normale Supérieure in Paris. Since 1997, she his a
researcher at CWI in Amsterdam.
Monique Laurent's research interests focus on combinatorial optimization and
discrete geometry. In particular, she has worked on polyhedral theory of cuts
in graphs, embeddings of metric spaces, metric aspects of
lattices, matrix completions, and semidefinite programming.
Part of this work has led to a coauthored book,
Geometry of Cuts and Metrics, published in 1997.

Title of the talk: Semidefinite relaxations for 0/1 polytopes.
Abstract: Several methods for constructing
linear and/or semidefinite relaxations of 0/1 polytopes
have been proposed; in particular, the liftandproject method
(Balas, Ceria and Cornuéjols),
the iterative matrixcut method (Lovász and Schrijver),
the RLT method (Sherali and Adams),
and some algebraic
methods based on representations
of polynomials as sums of squares and the dual theory of moments
(Lasserre, Parrilo, Shor).
We show that the tightest relaxations are obtained when applying
the algebraic construction and give a simple combinatorial
interpretation in the 0/1 case.
We study in detail an application to the maximum cut problem.
Several results are presented, including
a linear lower bound on the number of iterations needed for
finding the cut polytope, and a geometric result on the set
of moment matrices.

Dominikus Noll
Pierre Apkarian

Dominikus Noll is a full professor of applied mathematics at
Université Paul Sabatier, Toulouse. His research interests
include feedback control, medical imaging, inverse problems
and nonlinear optimization.
Coauthor Pierre Apkarian is a research engineer at ONERA
Toulouse, and a part time professor of applied mathematics
at Université Paul Sabatier. His research interest are
in automatic control and nonlinear optimization.

Title of the talk:
Feedback control design via nonlinear programming
Abstract:
Many problems in feedback control may be cast
as mathematical programs under matrix inequality constraints.
The most prominent example is Hinfinty synthesis,
which may be solved by semidefinite programming (SDP).
In this talk we will look at more complicated cases like robust
output feedback control synthesis and reduced order synthesis,
which are NPhard problems and require approaches beyond
SDP. We discuss algorithms suited to solve these difficult
problems. A typical test example in satellite attitude control
is presented.

Pablo Parrilo

Pablo A. Parrilo was born in Buenos Aires, Argentina. He received the
Electronics Engineering degree from the University of Buenos Aires in 1994,
and a PhD in Control and Dynamical Systems from the California Institute of
Technology in June 2000. He held shortterm visiting appointments at UC
Santa Barbara, Lund Institute of Technology, and UC Berkeley. In October
2001, he joined the Automatic Control Department of the Swiss Federal
Institute of Technology (ETH Zurich) as an Assistant Professor.
His research interests include robust control and identification,
robustness analysis, networked systems, convex optimization and
computational algebra.

Title of the talk:
Sums of squares and zero dimensional ideals.
Abstract:
In practice, many polynomial optimization problems have additional algebraic
properties that, suitably exploited, allow for much more efficient
algorithms. In this talk, we will focus on how equality constraints can be
exploited within the sum of squares / semidefinite programming framework. In
this case, using a quotient basis, all computations can be done in the
coordinate ring, notably decreasing the computational burden. As a
consequence, for zero dimensional systems, we obtain a simple constructive
proof of the existence of distinguished sum of squares representations for
polynomials nonnegative over semialgebraic sets. Degree bounds are directly
obtained, as the cardinality of the support of the summands equals the
number of points in the variety.

Jos Sturm

Jos F. Sturm completed his academic studies in Econometrics at the
University of Groningen, Groningen, The Netherlands in 1993, and
received the Ph.D. degree from Erasmus University, Rotterdam, The
Netherlands in 1997.
He has been an assistant professor at
Maastricht University and a postdoc at McMaster University.
He is currently an associate professor in the Department of
Econometrics and Operations Research at Tilburg University,
Tilburg, The Netherlands.
His research interests are in large scale
optimization, cone linear programming, robust optimization and
interior point methods.
Dr Sturm was awarded the Gijs de Leve Prize for the best thesis in
Operations Research in The Netherlands in the years 19971999, and has
received research grants from The Netherlands Organisation for
Scientific Research (NWO).

Title of the talk:
A new variant of the interior point method, for large scale and
warm started linear programs.
Abstract:
A new variant of the interior point method is proposed. While using a
low rank update scheme, the iterates are both powerful and
inexpensive to compute. The low rank updates are realized through a
product form factorization. The new algorithm is particularly useful
when it is initialized from a warm start.
