SMALLEST NONNEGATIVE SOLUTIONS TO LINEAR INVERSE PROBLEMS

Physical considerations often dictate nonnegativity for solutions to linear geophysical inverse problems. Applying the Lagrange multiplier theorem, the nature of that nonnegative solution is deduced, which is smallest in the 2-norm sense. The two-data inverse problem of inference of a planetary density profile, from measurements of mass and moment-of-inertia, serves to show the existence of nonextremal, nonnegative solutions that also satisfy the Lagrange multiplier condition. Numerical exploration indicates which of this family is the true extremal solution.