The paper presents some main aspects regarding multi-parametric quadratic programming (mp-QP) problems. Model Predictive Control (MPC) is considered as a particular mp-QP problem, and this powerful tool is applied for control and simulation through a case study. Since the solutions to mp-QP problems can be expressed as piecewise affine linear functions of the state, a new implementation in term...

The goal of multi-parametric quadratic programming (mpQP) is to compute analytic solutions to parameter-dependent constrained optimization problems, e.g., in the context of explicit linear MPC. We propose an improved combinatorial mpQP algorithm that is based on implicit enumeration of all possible optimal active sets and a simple saturation matrix pruning criterion which uses geometric propert...

A resource allocation model (RAM) for not-for-profit organization in the framework of Data Envelopment Analysis (DEA) was introduced by Zhang and Cui ([1]). The model is an inverse formulation to the DEA model , as pointed in paper [2], and can be transformed into a parametric linear programming problem. Also a multi-objective programming problem was introduced in [2] to solve RAM when the effi...

Data envelopment analysis (DEA) is a non-parametric technique for evaluation of relative efficiency of decision making units described by multiple inputs and outputs. It is based on solving linear programming problems. Since 1978 when basic DEA model was introduced many its modifications were formulated. Among them are two or multi-stage models with serial or parallel structure often called net...

A numerical algorithm for approximate multi-parametric nonlinear programming is developed. It allows approximate solutions to nonlinear optimization problems to be computed as explicit piecewise linear functions of the problem parameters. In control applications such as nonlinear constrained model predictive control this allows efficient online implementation in terms of an explicit piecewise l...