Solving inverse cone-constrained eigenvalue problems

We compare various algorithms for constructing a matrix of order n whose Pareto spectrum contains a prescribed set Λ = {λ1, . . . , λp} of reals. In order to avoid overdetermination one assumes that p does not exceed n2. The inverse Pareto eigenvalue problem under consideration is formulated as an underdetermined system of nonlinear equations. We also address the issue of computing Lorentz spectra and solving inverse Lorentz eigenvalue problems. Mathematical subject classification: 15A18, 65F18, 65H17.