Abstract

Optimization problems prevail in all kinds of technology. Nature also prefer optimization in formulating its laws in the form of variational principles. It is for these reasons that optimization should be considered to be of highest priority to be studied in mathematics and to be recommended in education. In fact, the preli- minary success of calculus over simple min-max problems is one of the readons that calculus is to be taught in all college-departments.

On the other hand, optimization is a very difficult problem for mathematics. Thus, even in very simple cases, the usual treatment by calculus will give only LOCAL conditions which are either necessary or sufficient alone, but not both.

We shall give a general method for the important POLYNOMIAL cases. Our method shows that the situation will become very agreeable in such cases for which we shall get even solutions of a GLOBAL character. Various kinds of applications will be given to illustrate the efficiency and feasibility of our method.