VIGRE Research Focus Group 2005-2006:

Optimization and Control



This is the main source of information regarding the research focus group in Optimization and Control. These areas are active fields of mathematics dealing with the problem of finding best solutions (according with some criterion) or the most stable configurations. For example, the problem of programming the automatic pilot of an airplane, the problem of matching crews with airline flights, or the problem of finding the shortest route to a destination are typical problems in the area. The goal of the RFG will be to introduce students (graduate and undergraduates) to these topics and show students the many career opportunities that these topics can offer. Here in the math department, and on campus, we have several strong subtopics that will be the primary source of activity:

  • Combinatorial & Integer Optimization.
  • Stochastic Optimization.
  • Large-scale optimization.
  • Control Theory.
  • Optimization Problems in Geometry and Topology (e.g. minimal surfaces).
  • Convexity & Optimization.
  • Randomized and Approximation Algorithms in Optimization.
  • Algebraic Techniques in Optimization (e.g. Representation theory for the study of Quadratic Assignment problems).
  • Applications in Computer Science and Engineering (e.g. compiler design).
  • Applications in Bioinformatics.
  • Applications in Management Sciences and Finances.

    This RFG is interdisciplinary and extends to the interest of many faculty members and graduate students from other departments. We hope it will help foster more interaction with them too.

    Main axiom of the RFG: Everyone is welcome to attend! Especially students!



    Participants

    Faculty: Zhaojun Bai (MATH/CS), Jesus DeLoera (lead faculty MATH), Roland Freund (MATH), Daniel Gusfield (CS), Joel Hass (MATH), Arthur Krener (MATH), Charles Martel (CS), Anne Schilling (MATH), Monica Vazirani (MATH), Roger Wets (MATH), David Woodruff (Business School).

    Graduate students: Susan Margulies, Tyrrell McAllister, David Haws, James Parmenter, Leslie Young, Deanna Needell.
    Undergraduate Students: David Karapeytan, Katherin Stalder, Michael Tehranian, Nicholas Nguyen, Daniel Hively.

    Activities

    The core activities all are mathematics courses, Math 168, Math 258AB, and a special Math 280 topics class. We will have regular research talks (Times TBA). In addition we will have:


    Fall 2005:
             
    Preliminary Exam Workshop (ALGEBRA/LINEARALG)
    Winter 2006:
    290/198: Reading seminar: "Algebraic Techniques in Optimization"
    Spring 2006:
    Summer 2006:
    RFG closing workshop (presentations by students).

    For suggestions or questions please contact Jesus De Loera.


    SEMINARS AND EVENTS OF THE RFG

    Oct 6, 4:40pm-6pm Wellman 105, Prof. Roger Wets (Mathematics UCD) Dealing with Uncertainty in Decision Making Models.

    Oct 7, 1:10-2pm Kerr 693, Prof. Jesus De Loera (Mathematics UCD) Transportation problems: A twenty year update.

    Oct 7, 4:10-5pm Kerr 693, Prof. Yinyu Ye (Stanford Operations Research) Theory and Computation of Semidefinite Programming for Sensor Network Localization and Graph Realization

    Oct 13 12:10-1pm Kerr 593, Prof. Arthur Krener (Mathematics UCD) A Brief Survey of Modern Nonlinear Control Theory.

    Oct 20 12:10-1pm Physics 140, Prof. Roland Freund (Mathematics UCD) Semidefinite Programming and the Design of Passive Linear Dynamical Systems

    Oct 27, 12:10PM Physics 140, David Woodruff, UC Davis School of Management, Mathematical descriptions of, and an algorithm for, making big decisions in the face of uncertainty in a dynamic world.

    Nov 3, 12:10pm, 140 Physics/Geol, Jiawang Nie, UC Berkeley Global Polynomial Optimization

    Nov 10, 12:10pm, 140 Geology/Phys, Dr. Sanjeeb Dash, IBM Watson Research center.Cutting planes for integer programming Nov 17, 12:10pm, 140 Physics/Geol, Prof. Gabor Pataki, University of North Carolina at Chapell Hill. Column basis reduction, and decomposable knapsack problems

    SEMINAR WINTER 2006

    The seminar will take place in the room 2112 of the Mathematical Sciences Building every Friday at 2pm. This time the seminar will have more active participation from students. We will be reading the third part (=Algorithms, Chapters 9,10,11) of the book ``Convex Optimization'' by Stephen Boyd and Lieven Vandenberghe, Cambridge University Press 2004. A few students expressed interest on reading and presenting from original research papers. I will be glad to help on preparing, etc. Here are a few suggestions:

    Review of Nonlinear Mixed-Integer and Disjunctive Programming Techniques by Ignacio Grossmann. This is a survey paper about practically solving non-linear mixed-integer problems.

    Error Correction via Linear Programming by Candes, Rudelson, Tao and Vershynin. The paper presents a novel approach to the problem of reliably recovering (no errors) sending a message vector f from the transmited vector Af+e.

    Fast Fourier Transform and its applications to integer Knapsack problems, by Yu. Nesterov. A new way to solve knapsack problems. (TAKEN by Isaiah)

    Smoothed Analysis of Algorithms: Why The Simplex Algorithm Usually Takes Polynomial Time, by Shang-Hua Teng, and Daniel A. Spielman The title says it all. It is a very interesting development.

    Semidefinite programming relaxations for semialgebraic problems. by P.A. Parrilo. The author explains how any optimization problem with polynomial constraints can be reduced to a sequence of approximations using Semidefinite programming problems (=convex optimization). (Taken by Dave Haws).

    Seminar Spring 2006

    We will meet every Friday, starting April 7, 12:10am to 1pm. With the exception of the first meeting (April 5) we will meet in Room 2112 MSB Will start by assigning papers to students to read and present. The first five weeks we have guest speakers

    3106 MSB (note! room change), Daniel Kuhn, Stanford University Wed, Apr 5 2006, 4:10PM, Aggregation and Discretization in Multistage Stochastic Programming

    Dr. Cipriano Santos, Hewlett-Packard Research Fri, Apr 7 2006, 12:10PM "Computing Resource Allocation at Large Scale Computing Distributed Environments"

    Prof. Jeff Linderoth, Lehigh University Fri, Apr 14 2006, 12:10PM Multistage Stochastic Linear Programming on a Computational Grid

    Dr. Matthias Koeppe, Univ. Magdeburg/ UC Davis Fri, Apr 21 2006, 12:10PM Fully polynomial time approximation schemes for mixed-integer polynomial optimization

    Ruriko Yoshida, Duke University Fri, Apr 28 2006, 12:10PM Fundamental holes and saturation points of a commutative semigroup and their applications to contingency tables.

    Week 6 (May 5):

    Dave Haws will present
    "The minimum weight triangulation is NP-hard"
    by
    http://theoryofcomputing.org/articles/main/v002/a002/a002.pdf

    Week 7 (May 12):

    will present
    "Towards Strong Nonapproximability Results in the Lovasz-Schrijver Hierarchy"
    Mikhail Alekhnovich and Sanjeev Arora and Iannis Tourlakis
    http://www.cs.princeton.edu/~arora/pubs/aat-stoc.pdf

    Week 8 (May 19):

    will present
    "Towards Strong Nonapproximability Results in the Lovasz-Schrijver Hierarchy"
    Mikhail Alekhnovich and Sanjeev Arora and Iannis Tourlakis
    http://www.cs.princeton.edu/~arora/pubs/aat-stoc.pdf

    Week 9 (May 26):

    presents
    "Towards Strong Nonapproximability Results in the Lovasz-Schrijver Hierarchy"
    Mikhail Alekhnovich and Sanjeev Arora and Iannis Tourlakis
    http://www.cs.princeton.edu/~arora/pubs/aat-stoc.pdf

    Week 10 (June 2):

    presents
    "Towards Strong Nonapproximability Results in the Lovasz-Schrijver Hierarchy"
    Mikhail Alekhnovich and Sanjeev Arora and Iannis Tourlakis
    http://www.cs.princeton.edu/~arora/pubs/aat-stoc.pdf