ABSTRACT
It has been proved that in non linear programming, there are five methods of solving multivariable optimization with constraints.
In this project, the usefulness of some of these methods (Kuhn – Tucker conditions and the Lagrange multipliers) as regards quadratic programming is unveiled.
Also, we found out how the other methods are used in solving constrained optimizations and all these are supported with examples to aid better understanding.
LAYOUT OF WORK
There are five chapters in this project.
Chapter two is dedicated to two methods of solving constrained optimization. These methods are the Lagrange multiplier method and the Kuhn-Tucker conditions. This section clearly shows how the Kuhn-Tucker conditions are derived from the Lagrange multiplier method, in an optimization problem with inequality constraints. As part of this chapter, the global maximum, local maximum and the global minimum of an optimization problem was also derived.
Chapter three presents the gradient methods and the method of feasible directions. The gradient methods are the Newton Raphson method and the penalty function.
The gradient methods are used in solving optimization problems with equality constraints while the method of feasible directions is used in solving optimization problems with inequality constraints.
Chapter four is specifically on a type of multivariable optimization with constraints. This is called “Quadratic programming”. This chapter comprises of quadratic forms, general quadratic problems and it shows the importance of two methods called the Lagrange multiplier method and the Kuhn-Tucker conditions. This section explains how we can arrive at an optimal solution through two different methods after the Kuhn-Tucker conditions have been formed. These are the two-phase method and the elimination method.
Chapter 5 is the concluding part of this project.
Each chapter starts with an introduction that facilitates the understanding of the section and also contains useful examples.
In conclusion, this research will make us understand the different methods of solving constrained optimization and how some of these methods are applied in quadratic programming.
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===================================================================Item Type: Project Material | Size: 124 pages | Chapters: 1-5
Format: MS Word | Delivery: Within 30Mins.
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