I present an algorithm for the one-dimensional magnetotelluric inverse problem of finding conductivity as a function of depth in the earth. The algorithm uses linear programming to solve an integral form of a nonlinear Riccati equation. This iterative scheme sacrifices the efficiency of direct inversion for the overwhelming advantages of incorporating localized conductivity constraints. I use localized conductivity constraints in two ways to combat the nonuniqueness of the nonlinear inverse problem. First, I impose physical constraints derived from external sources to restrict the nonuniqueness and construct conductivity models that are closer to reality. Second, I impose arbitrary constraints in an effort to assess the extent of nonuniqueness and explore the range of acceptable profiles. The first technique enhances the reliability of an interpretation, and the second measures the plausibility of particular conductivity features.