Particulars of Non-Linear Optimization

Abstract

We are providing a concise introduction to some methods for solving non-linear optimization problems. In mathematics,non-linear programming (NLP) is the process of solving an optimization problem defined by a system of equalities and inequalities, collectively termed constraints, over a set of unknown real variables, along with an objective function to be maximized or minimized, where some of the constraints or the objective function are non-linear. It is the sub-field of mathematical optimization that deals with problems that are not linear. This dissertation conducts its study on the theory that are necessary for understanding and implementing the optimization and an investigation of the algorithms such as Wolfe's Algorithm, Dinkelbach's Algorithm and etc. are available for solving a special class of the non-linear programming problem, quadratic programming problem which is included in the course of study. Optimization problems arise continuously in a wide range of fields such as Power System Control and thus create the need for effective methods of solving them. We discuss the fundamental theory necessary for the understanding of optimization problems, with particular programming problems and the algorithms that solve such problems.