Algorithms for Constructing Optimal on Volume Ellipsoids and Semidefinite Programming

Abstract

The solution of problems of constructing optimal with respect to the volume circumscribed and inscribed ellipsoids is of great interest due to the broad range of their applications. Primarily these problems can be used to define the “upper” and “lower” approximations of convex sets, for example, the regions of attainability in the theory of control and differential games; to refine regions of localization of possible values of dynamic system parameters, using a priori information and results of measurements [Ch 88]; then in statistics, in planning experiments to determine parameters of regression models [Fed 71], in numerical mathematics to describe sets of possible solutions of linear and nonlinear equations with perturbed coefficients, [FF 60], etc.