Presented in this paper is an optimization technique for solving problems with objective functions which are sums of squared quantities with linear constraints. The technique is based on Gauss’ unconstrained method, but is able to move along constraint surfaces in such a way that when the technique terminates, the Kuhn-Tucker conditions are satisfied. The resulting approach, called the Gauss constrained method, is shown to be very efficient and effective in solving problems with highly nonlinear objective functions often existing in mechanism design problems.

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