Differential equations approach in constraint minimization

In this paper a discussion of relatively new class of methods dealing with constraint minimization problems is presented. The genesis of this new class arises from the requirement of solving a system of nonlinear equations which is equivalent to solving a system of related differential equations. The solution of this system of differential equations has a continuous curvilinear are and aonsequently a steepest descent curve is obtained. From a practical point of view an approximation of the descent curve is made which has the advantages, viz., not requiring the inversion of Hessian and a descent in the value of the objective is guaranteed irrespective of the character of the Hessian matrix. A numerical result is also presented.