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Subspace Frameworks for Eigenvalue Optimization and Applications

  • Date May 31, 2018
  • Hour 3 pm
  • Room GSSI Main Lecture Hall
  • Speaker Emre Mengi (Koc University, Turkey)
  • Area Mathematics

ABSTRACT

We deal with a Hermitian matrix depending on parameters, and the minimization of its jth largest eigenvalue (for a prescribed j) over the set of admissible parameter values. Such problems have drawn substantial interest starting around the 1980s due to their connection with semi-definite programs, more recently due to applications in robust control. A major hurdle today is how to cope with such problems in the large-scale setting, that is when the parameter-dependent matrix is large. The talk describes procedures to construct small subspaces such that the projection and restriction of the parameter-dependent matrix into these subspaces lead to reduced eigenvalue Optimization problems that approximate the original optimization problem well. The proposed subspace procedures are greedy interpolatory approaches; they are designed to achieve rapid global convergence with respect to the subspace dimension in theory. In the second part of the talk, we present adaptations of the subspace procedures for large-scale semi-definite programs and for the
maximization of the robust stability of linear dynamical systems.