VARIATIONAL ANALYSIS OF AN EXTENDED EIGENVALUE PROBLEM

For a symmetric matrix B is an element of R(nXn) and a vector a is an element of R(n), the maximal extended eigenvalue lambda(a) :=max{lambd a : There Exists x is an element of R(n) s.t. (B - lambda I)x = a, x(t )x = 1}, is known to arise in optimality conditions for the mathematic al programming problem P(a) given by max{x(t)Bx - 2a(t)x : x(t)x = 1}, as well as in extended Rayleigh-Ritz type results pertaining to the o ne parameter family of nonsymmetric border perturbations of B given by [GRAPHICS] Nonsmooth analysis is employed in order to describe the fu nction lambda(.), with special emphasis on its sensitivity near the or igin. Further connections with P(a) are drawn.