comparative study of penalty functions for non linear quadratic programming

Abstract

newlineOptimization refers to selection of best alternatives from available list of alternatives in a decision making problem. Optimization can be considered as situation in which a given quantity has to be evaluated for maximization and minimization under certain conditions. Optimization has an important application in decision theory and helps in taking swift and correct decisions while dealing with physical systems. Optimization is a mathematical tool whose application on various problems begins with the proclamation of the objective function which symbolises the qualitative measurement of the capability of the system under observation. The objective defined can be any scalar quantity or a linear combination of various other quantities represented as a monomial quantity. To achieve the objective of the problem certain features are framed as variables. The process of optimization is to find a set of values of these variables which helps in achieving the targeted objective. Various restrictions are applied on the variables in terms of cost, expenditure etc. which leads to the formation of constraints. The whole procedure of defining objective function, variables and constraints is called as mathematical modelling.