The Weak Sharp Of Solution Set For Multi-Parametric Programming

Parametric programming is widely used in Predictive Control.Its theory and practical application are remarkable.This paper systematically studies the multi-parametric programming problem,including multi-parametric linear programming,multi-parametric nonlinear programming.The properties of weakly sharp sets in multi-parametric programming problems are analyzed,The necessary and sufficient conditions for the convergence of the algorithm are obtained.First,the second chapter considers two kinds of multi-parametric linear programming problems.For two different kinds of multi-parametric linear programming problems,the definition of weakly sharp sets of multi-parametric linear programming problems is given respectively.Then,we analyze the situation of the weakly sharp set with the vector parameter change,and obtain the equivalence condition of weakly sharp set.Next,the third chapter considers the problem of quadratic programming for the multi-parametric programming,mainly for the sequence quadratic programming sub-problems with vector parameters.The definition of weakly sharp in the quadratic programming sub-problem is given,and the properties of weakly sharp are analyzed,and the necessary and sufficient conditions for the finite convergence of the algorithm is obtained.In the fourth chapter,we consider the general multi-parametric programming problem.We mainly discuss the case that the objective function is a semi-continuous function or a composite semi-continuous function.We analyze the properties of the weakly sharp set and obtain the equivalence condition of the weakly sharp set.