A Lagrangian algorithm for equality constrained generalized polynomial optimization

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Abstract
A procedure for optimizing generalized polynomial functions occurring widely in engineering design problems is presented. Equality constraints of the same form can be handled. The technique involves driving to zero the gradient of a Lagrangian function by a Newton‐Raphson method. A nonlinear transformation so simplifies the derivatives needed for Newton‐Raphson iteration that they are given in closed form. The initial estimate needed to start the algorithm need not be feasible. Successive systematic adjustment of Lagrange multipliers is accomplished, and an unambiguous procedure for starting multipliers is given. All implicit computations are linear. Convergence is not proven, but successful computational results for the design of a reactor exchanger pump system in eight variables and with five constraints are presented.

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