Graduate Student Sessions in Optimization

Current List of Participants:

  • Heinz Bauschke, Simon Fraser University FINDING SUPPORT IN HILBERT SPACE This talk is an advertisement for Fejer monotonicity; a concept that is not only geometrically appealing but - more importantly - quite useful. Fejer monotone sequences arise, for instance, in Fixed Point Theory (iterates of nonexpansive mappings) and in Convex Optimization (projection algorithms). I will describe an algoritm (developed with Jon Vanderwerff) that solves the "support point problem": Given a functional and a closed convex subset of a Hilbert space, find a corresponding support point. I will attempt to give a self-contained proof of a convergence result on this algorithm; this proof (of course) relies on Fejer monotone sequences.

  • Negash Begashaw, Washington State University GLOBAL CONVERGENCE OF COLLINEAR SCALING ALGORITHMS UNDER INEXACT LINE SEARCHES We present an extension of the results on global convergence of Byrd, Nocedal and Yuan (1987) for quasi-Newton methods to a family of collinear scaling algorithms derived by Ariyawansa (1990) under line search termination criteria proposed by Ariyawansa (1994).

  • Mark Coodey (jointly with Stephen Simons), University of California at Santa Barbara Pictures of monotone operators Let $E$ be a nontrivial Banach space. We will define the picture of any nonempty subset of $E\times E^*$. This picture is a convex subset of the plane. The concept of ``picture'' has been used to provide a new proof of the surjectivity of $S+J$, for $E$ reflexive and $S : E \to 2^{E^*}$ maximal monotone. It is known that if $E$ is reflexive, then the picture of a maximal monotone subset of $E \times E^*$ is a singleton. We calculate an example showing that in the nonreflexive case the picture of a maximal monotone subset can be quite substantial.

  • Peilei Jiang, Washington State University ON THE COMPLEXITY OF AN ALGORITHM FOR CONVEX MINIMAX OPTIMIZATION Burke, Goldstein, Tseng and Ye recently presented an interior point algorithm for the smooth convex minimax problem. Their algorithm is based on analytic centers. Unlike in other algorithms the criterion they use to specify ``inexact analytic centers" is independent of problem dependent constants. However the assumptions made in their analysis to estimate the total work to obtain a solution within epsilon of the minimum makes their criterion dependent on constants that may be hard to estimate. Moreover, the analysis does not indicate how the total work depends on problem dimensions. In this paper, we state a simple criterion that depends only on a user specified tolerance. We explicitly indicate how the total work depends on problem dimensions.

  • Michael Monagan, Simon Fraser University Automatic Differentiation and The Reverse Mode Algorithm

  • Jennifer Mueller, University of Nebraska at Lincoln An application of a Levenberg-Marquardt algorithm to a parameter-recovery problem on the real line

  • David Salinger, University of Washington An Operator Splitting Algorithm for the Multistage Stochastic Programming Problem The focus here will be on some of the main theoretical results which lead to the development of the algorithm. Rather than present a general Stochastic Programming model, I will talk briefly about the hydroelectric power generation scheduling problem as an example of such models. Then the algorithm develpment goes as follows: reformulate the model as a saddle point problem on the reduced Lagrangian, carefully apply an operator splitting scheme to the resulting convex-concave saddle point problem, and exploit the structure of the resulting subproblems.

  • Andrei Vityaev, University of California at San Diego and University of Washington ON OPTIMIZATION PROBLEMS IN SIGNAL PROCESSING IN MAGNETIC RECORDING AND DIGITAL COMMUNICATIONS We give a short discussion of several optimization problems arising in the decoder design for convolutional codes. Optimization problems range from linear programming to general non-linear convex optimization.

  • Andreas Wiegmann, University of Washington LIMITED MEMORY QUASI-NEWTON METHODS IN A TRUST-REGION FRAMEWORK

  • Song Xu, University of Washington ALGORITHMS FOR BOX CONSTRAINED OPTIMIZATION PROBLEMS

  • Min Zhu, Washington State University SELF-COMPLEMENTARY VARIABLE METRIC ALGORITHMS

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