Three optimization techniques of mathematical programming



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Since World War II, mathematical programming has steadily increased in solution methods and scope of application. Mathematical programming has been extended from economic analysis into structural design, communications systems, transportation systems, and personnel assignments, to name but a few. It is, therefore, important that today's engineers understand the basic concepts as well as the problem formulations that are inherent in mathematical programming. Thus, the objective of this thesis is to present three methods of optimization; namely, simplex method, Lagrange multiplier method, and gradient method which may be used for both linear and nonlinear mathematical programming. With this information, today's engineers, even those with a somewhat limited mathematical background, may gain insight into the various solution techniques. A literature survey was made from which the basic theorems and proofs were derived to substantiate the various solution techniques. The survey was by no means exhaustive, and the methods presented are only the basic facts upon which to build knowledge and experience. Numerical examples are presented to demonstrate the solution techniques of the simplex method, the Lagrange multiplier method, and the gradient method as applied to linear programming, as well as the Lagrange multiplier method, and. the gradient method as applied to nonlinear programming.