Multiparametric Linear and Quadratic Programming

In this work we present an algorithm for the solution of multiparametric linear and quadratic programming problems.With linear constraints and linear or convex quadratic objective functions, the optimal solution of these optimization problems is given by a conditional piecewise linear function of the varying parameters. This function results from first-order estimations of the analytical nonlinear optimal function. The core idea of the algorithm is to approximate the analytical nonlinear function by affine functions, whose validity is confined to regions of feasibility and optimality. Therefore, the space of parameters is systematically characterized into different regions where the optimal solution is an affine function of the parameters. The solution obtained is convex and continuous. Examples are presented to illustrate the algorithm and to enhance its potential in real-life applications.