A study on linear complementarity problems and its applications

Abstract

The proposed research work focuses its attention to a study on Linear newlineComplementarity problems in fuzzy and Intuitionistic fuzzy environment. The thesis newlinewill stress the importance and need to consider the topics like Linear Programming, newlineQuadratic Programming and Multi-objective Linear Programming problem with fuzzy newlineand intuitionistic fuzzy numbers. Many practical problems cannot be represented by newlinelinear programming model. Therefore the Linear Complementarity problem developed newlinefor both linear and non linear cases. Study and solve the Linear Complementarity newlineproblems using triangular, trapezoidal, symmetric trapezoidal intuitionistic fuzzy newlinenumber and neutrosophic number. newlineIn this thesis, we have obtained the optimal solution for the Linear newlineComplementarity problem using different kinds of ranking functions. It is proposed to newlinesolve the given non linear programming problem using Lemke s algorithm. Algebraic newlineelimination method is used to determine the best compromise solution to a Linear newlineComplementarity problem. The variable dimension algorithm provides the solution of newlineLinear Complementarity problem in different kinds of dimension. Principal pivoting newlinemethod applied for solving the Linear Complementarity problem and further it can be newlineused to find the inverse of the basis. High and low penalty methods are developed for newlinesolving linear complementarity problem. newline