Multidimensional Line Search Using a Binary Preference Relation

A number of interactive algorithms involving line searches have recently been suggested for use when the decision-maker's preferences take the form of a binary relation rather than the standard criterion function. This study examines the extension of well-known line-search procedures based on a criterion function to binary representations for preference and briefly outlines why some procedures are not extendible. Extensions of uniform and golden section line-search procedures are examined in detail. Knowledge of these extensions should assist the user of interactive algorithms to select a line-search procedure that is appropriate for his needs.