Optimizers for Sub-Sums subject to a Sum- and a Schur-Convex Constraint with Applications to Estimation of Eigenvalues

A complete solution is presented for the problem of determining the sets of points at which the functions (x1, . . . , xn) → xk + . . . + xl, subject to the constraints M x1 . . . xn m, x1 + x2 + . . . + xn = a, and g(x1) + g(x2) + . . . + g(xn) = b, with g strictly convex continuous, assume their maxima and minima. Applications are given. Mathematics subject classification (2000): 90C25, 26D15, 15A42.