Monday, May 10

Primal-Dual Interior Point Methods for Optimization Problems with Semidefinite, Quadratic and Linear Constraints - Part I of II

10:45 AM-12:45 PM
Room: Capitol Center

For Part II, see MS11.

In the past several years, a close kinship among linear, semidefinite, and convex quadratically constrained programming has emerged. Already it had been recognized that the potential reduction methods of linear programming can be extended to such optimization problems with little modification. However primal-dual methods, which incidentally remain the method of choice for virtually all practical implementations of interior point methods, yield a much more intricate and elaborate theory when any combination of linear, quadratic or semidefinite constraints are present. Indeed, there is an infinite class of such primal-dual algorithms and both their analysis and their practical merits are subjects of intensive research. Also intriguing is the connection to the theory of Euclidean Jordan algebras. The speakers in this two-part minisymposium will report on the latest developments in primal-dual algorithms, including the recent breakthroughs in computational complexity analysis, numerical stability properties, and Jordan algebraic perspective.

Organizers: Farid Alizadeh
Rutgers University
Renato Monteiro
Georgia Institute of Technology

10:45-11:10 On the Numerical Integration of Affine-Scaling Vector Field
Leonid Faybusovich, University of Notre Dame
11:15-11:40 New Types of Interior-Point Methods for Linear Programming
Ming Gu, University of California, Los Angeles
11:45-12:10 Primal-Dual Path-Following Algorithms for Second-Order Cone Programming
Takashi Tsuchiya, The Institute of Statistical Mathematics, Japan
12:15-12:40 Associative Algebras, Symmetric Cones and Interior-Point Algorithms
Stefan Schmieta, Rutgers University; and Farid Alizadeh, Organizer

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MMD, 12/17/98