The Variable Reduction Method for Nonlinear Programming

A first-order method for solving the problem: minimize f(x) subject to Ax − b ≧ 0 is presented. The method contains ideas based on variable reduction with anti-zig-zagging and acceleration devices based on the Variable Metric Method. Proof of convergence to a Kuhn-Tucker Point, and statement of the rate of convergence when the strict second order sufficiency conditions hold are given.