610 HESFCN -- A FORTRAN PACKAGE OF HESSIAN SUBROUTINES FOR TESTING NONLINEAR OPTIMIZATION SOFTWARE V. Averbukh, S. Figueroa, T. Schlick, June 1992 We report the development of Hessian FORTRAN routines for testing unconstrained nonlinear optimization. An existing package, "Algorithm 566" (J. Mor'e, B. G. Garbow, and K. Hillstrom, ACM Trans. Math. Softw. 7, 14-41 and 136-140, 1981) provides function and gradient subroutines of 18 test functions for multivariate minimization. Our supplementary Hessian segments will enable users to test optimization software that requires second derivative information. Eigenvalue analysis throughout the minimization will also be possible in the goal of better understanding minimization progress by different algorithms and the relation of progress to eigenvalue distribution and condition number.