Abstract
Optimization problems with maximum eigenvalue or singular eigenvalue cost or constraints occur in the design of linear feedback systems, signal processing, and polynomial interpolation on a sphere. Since the maximum eigenvalue of a positive definite matrix Q(x) is given by max‖y‖=1〈(y, Q(x)y〉, we see that such problems are, in fact, semi-infinite optimization problems. We will show that the quadratic structure of these problems can be exploited in constructing specialized first-order algorithms for their solution that do not require the discretization of the unit sphere or the use of outer approximations techniques.
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© 2001 Springer Science+Business Media Dordrecht
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Polak, E. (2001). First-Order Algorithms for Optimization Problems with a Maximum Eigenvalue/Singular Value Cost and or Constraints. In: Goberna, M.Á., López, M.A. (eds) Semi-Infinite Programming. Nonconvex Optimization and Its Applications, vol 57. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3403-4_9
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DOI: https://doi.org/10.1007/978-1-4757-3403-4_9
Publisher Name: Springer, Boston, MA
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