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Algorithm for Minimizing a Convex Function of Two Integer Variables

IP.com Disclosure Number: IPCOM000047305D
Original Publication Date: 1983-Oct-01
Included in the Prior Art Database: 2005-Feb-07

Publishing Venue

IBM

Related People

Authors:
Hoffman, AJ Wolfe, PS [+details]

Abstract

This optimization algorithm determines the respective integer values of two real variables which will cause a given convex function of these two variables to have a minimum value, under conditions where the value of the function can be calculated only for integer arguments, and the gradient of the function cannot be calculated. As its initial input, the algorithm requires merely the finite values of the function for two points thereon which have integer-valued coordinates on the argument axes. From this initial information, the algorithm proceeds in a systematic manner to find a pair of integers which will yield a value of the two-variable function that approximates as nearly as possible the true minimum value of the function.