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This paper is concerned with the computational problem of maximizing the yield of circuits. A statistical Monte Carlo based approach is taken in order to compute yield estimates directly and to decrease dimensionality dependence. The main contribution of this paper is a yield extrapolation technique which is very effective in maximizing the yield along a search direction. This technique is based upon a quadratic model of the circuit. Statistical yield estimates are computed from the model and correlated sampling is used to extrapolate along the search direction. Two simple methods for determining search directions are discussed and these are used to demonstrate the overall method through several examples.