Optimization of a response variable y constrained by principal directions of variations in the observation X-matrix

A method for optimization constrained by principal directions of variations in an observation X-matrix is developed. The optimization has the form of a linear program/linear programs, where the constraints describing the infl uence of one variable on the others are given by one PLS component or a com bination of several. In the case of more than one PLS component included in the optimization, a stepwise optimization is performed, making a new PLS c omponent constraint with new loadings before each optimization. A solution of the optimization is achieved by letting the new loadings be equal to lin ear combinations of the original ones, and a search for the linear combinat ion giving the optimal point is performed. As an example, an optimization o f the compressive strength of cement as a function of the particle size dis tribution is shown. The function is a result of partial least squares regre ssion (PLS) on 120 observations. Copyright (C) 2000 John Wiley & Sons, Ltd.