New First-Order Algorithms for High-Dimensional
Quadratic Optimization

Victor Tolstykh

Computer Scince Department, Donetsk State University
Universitetskaya-24, 83055 Donetsk, Ukraine


Abstract

The new 1-st order optimization methods for high-dimensional unconstrained quadratic objective functions are described (draft paper is *ps.zip - 86K and *dvi.zip - 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 and test software for MS DOS . 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.