Variational analysis of an extended eigenvalue problem Original Research Article

For a symmetric matrix B set membership, variant Rn × n and a vector a set membership, variant Rn, the maximal extended eigenvalue λ(a):=max⁡{λ:there existsxset membership, variantRns.t.(B−λI)x=a,xtx=1}, is known to arise in optimality conditions for the mathematical programming problemP(a) given bymax⁡{xtBx−2atx:xtx=1}, as well as in extended Rayleigh-Ritz type results pertaining to the one parameter family of nonsymmetric border perturbations ofB given byimage Nonsmooth analysis is employed in order to describe the function λ(·), with special emphasis on its sensitivity near the origin. Further connections with P(a) are drawn.