POLYNOMIAL PENALTY METHOD FOR SOLVING LINEAR PROGRAMMING PROBLEMS

Abstract

In this work, in order to solve linear programming problems we study a class of polynomial order-even penalty functions for solving linear programming problems with the essential property that each member is convex polynomial order-even when viewed as a function of the multiplier. Under certain assumption on the parameters of the penalty function, we give a rule for choosing the parameters of the penalty function. We also give the first ordered necessary conditions with an algorithm for solving this problem. Therefore, the report consists of four parts. The first part deals with the introduction of polynomial penalty method; background, statement of the problem, objectives and methodology The second part of the report deals with some mathematical preliminaries that explains the definition, theory, properties of different topics which gives guide lines for polynomial ordereven penalty functions. The third part of the report deals with polynomial penalty method for solving linear programming problems which illustrate by giving appropriate examples and approaches to show the method. Finally the fourth part of the report discuss about the summary of the study that sum up the overall concepts of this seminar and which is presented as a general conclusion of the study