Positive Semidefiniteness and Positive Definiteness of a Linear Parametric Interval Matrix

Abstract

We consider a symmetric matrix, the entries of which depend linearly on some parameters. The domains of the parameters are compact real intervals. We investigate the problem of checking whether for each (or some) setting of the parameters, the matrix is positive definite (or positive semidefinite). We state a characterization in the form of equivalent conditions, and also propose some computationally cheap sufficient\,/\,necessary conditions. Our results extend the classical results on positive (semi-)definiteness of interval matrices. They may be useful for checking convexity or non-convexity in global optimization methods based on branch and bound framework and using interval techniques.

Cited by in corpus (5)

• Properties of the solution set of absolute value equations and the related matrix classes
• Stability of the linear complementarity problem properties under interval uncertainty
• An Overview of Polynomially Computable Characteristics of Special Interval Matrices
• Necessary and sufficient conditions for regularity of interval parametric matrices
• Positive definiteness and stability of parametric interval matrices