The Almighty has created the Universe and things present in it with an
order and proper positions and the creation looks unique and perfect. No one
can even think much better or imagine to optimize these further. People
inspired by these optimum results started thinking about usage of
optimization techniques for solving their real life problems. The concept of
constraint optimization came into being after World War II and its use
spread vastly in all fields. However, in this process, still lots of efforts are
needed to uncover the mysteries and unanswered questions, one of the
questions always remains live that whether there can be a single method that
can solve all types of nonlinear programming problems like Simplex
Method solves linear programming problems. In the present thesis, we have
tried to proceed in this direction and provided some contributions towards
this area.
The present thesis has been divided into five chapters, chapter wise
summary is given below:
Chapter-1 is an introductory one and provides genesis of the
Mathematical Programming Problems and its use in Statistics.
Relationship of mathematical programming with other statistical
measures are also reviewed. Definitions and other pre-requisites are
also presented in this chapter. The relevant literature on the topic has
been surveyed.
Chapter-2 deals with the two dimensional non-linear programming
problems. We develop a method that can solve approximately all type
of two dimensional nonlinear programming problems of certain class.
The method has been illustrated with numerical examples.
Chapter-3 is devoted to the study of n-dimensional non-linear
programming problems of certain types. We provide a new method
based on regression analysis and statistical distributions. The method
can solve n-dimensional non-linear programming problems making
use of regression analysis/co-efficient of determination.
In chapter-4 we introduce a filtration method of mathematical
programming. This method divides the constraints into active and non
active and try to eliminate the less important constraints (non-active
constraints) and solve the problem with only active constraints. This
helps to find solution in less iterations and less in time while retaining
optimality of the solution.
The final chapter-5 deals with an interesting relationship between
linear and nonlinear programming problems. Using this relationship,
we can solve linear programming problems with the help of non-linear
programming problems. This relationship also helps to find a better
alternate solutions to the linear programming problems.
In the end, a complete bibliography is provided
