The new 1-st order optimization methods for high-dimensional unconstrained quadratic objective functions are described. Draft paper is available in two forms, \verb2ftp://ftp.dongu.donetsk.ua/pub/faculty/physical/kkt/tolstykh/paper_ps.zip2 (86K) \newline \verb2ftp://ftp.dongu.donetsk.ua/pub/faculty/physical/kkt/tolstykh/paperdvi.zip2 (24K). These methods are constructed on original treatment of a necessary conditions for optimality. There are comparative computing test with a steepest descent method, conjugate gradient method, finite difference Newton method.

There are Internet URLs at author's home page \verb9http://www.dongu.donetsk.ua/fizfak/kkt2/tol.htm9 and test software for MSDOS, \verb9ftp://ftp.dongu.donetsk.ua/pub/faculty/physical/kkt/tolstykh/min-test.arj9. You can input dimension, function minimization method, initial guess and you will watch a descent track at function's level lines with normed gradients. The new methods show unique effective results for high-dimensional functions.