Estimating individual cone sensitivities on the basis of their corresponding individual color matching functions is a classic problem of color vision. To solve the problem one has, in effect, to postulate constraints on the shape of the cone sensitivities. For example, Logvinenko applied a linear matching method (originally proposed by Bongard and Smirnov [4]) which excludes all but one primary to which each of the sensitivities of the visual system is supposedly sensitive and, mathematically, if this constraint is met reasonable estimates should result. However, when applied to color matching functions in general, it turns out that the method estimates middle and especially long wave sensitivity quite poorly. We propose a new method based on linear optimization, in which it is assumed only that the photo-pigment spectral absorptance functions are known a priori. In an iterative scheme, the method works by simultaneously estimating the coefficients of the linear relation between the known individual color matching functions and estimated cone sensitivities and estimating the ocular and macular filtering that multiplied by the absorptances yield the estimated cone sensitivities. The ocular and macular pre-filtration is treated as a single spectral function (i.e. a combined ocular and macular filtration). We are also able to predict the cone sensitivities proposed by Stockman and Sharpe in recent research. The method is tested on a selection of individual 1959 10 degree Color Matching Functions, with the assumption that they have the Stockman and Sharpe 10 degree photo-pigment spectral absorbtance in common. The results for the estimated cone sensitivities look very plausible. Finally we have applied the method to the CIE1964 10 degree observer and get very reasonable result as well.