Using alpha-cuts and constraint exploration approach on quadratic programming problem

Abstract

In this paper, we propose a computational procedure to find the optimal solution of quadratic programming problems by using fuzzy α-cuts and constraint exploration approach. We solve the problems in the original form without using any additional information such as Lagrange's multiplier, slack, surplus and artificial variable. In order to find the optimal solution, we divide the calculation in two stages. In the first stage, we determine the unconstrained minimization of the quadratic programming problem (QPP) and check its feasibility. By unconstrained minimization we identify the violated constraints and focus our searching in these constraints. In the second stage, we explored the feasible region along side the violated constraints until the optimal point is achieved. A numerical example is included in this paper to illustrate the capability of α-cuts and constraint exploration to find the optimal solution of QPP.