An algorithm is derived to solve the constrained nonlinear programming problem. It is based on the properties of a class of algorithms that transform the constrained problem into a sequence of related unconstrained problems. It is envisaged that its main application will be to those problems where the number of evaluations of the functions involved are at a premium. Variants of the algorithms, however, are obtained to suit those problems where this may not be the case. There is a paramount need for such algorithms in a wide variety of fields, such as, engineering design, management science and the control of chemical processing plant. The complexity of the problem is such that even an algorithm suitable for very limited application would be useful if its limitations could be precisely determined.