Multivariable Optimization With Constraints

Project and Seminar Material for Mathematics and Statistics

Multivariable Optimization With Constraints


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.


Chapter Five


Conclusion

This research is aimed at providing a better understanding of the methods of solving constrained optimization.
It also gives an insight into the optimality conditions of quadratic programming.

Quadratic programming as a type of constrained multivariable optimization is applied in economics, management science, operations research literature, and also in financial analysis like the (basic portfolio model).

Now, based on the two types of constraints we have in this research, we found out that the gradient methods (Newton-Raphson method and penalty function) are used in solving optimization problems with equality constraints. The method of feasible directions is used in solving optimization problems with inequality constraints, the Lagrange multiplier method and the Kuhn-Tucker conditions are also useful in constrained optimization.


Multivariable Optimization With Constraints


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