The fundamental problem of distance geometry asks to find a realization of a finite, but partially specified, metric space in a Euclidean space of given dimension. Unless some structure is known about the structure of the instance, it is notoriously difficult to solve these problems computationally, and most methods will either not scale up to useful sizes, or will be unlikely to identify good solutions. We propose a new heuristic algorithm based on a semidefinite programming formulation, a diagonally-dominant inner approximation of Ahmadi and Hall's, a randomized-type rank reduction method of Barvinok's, and a call to a local nonlinear programming solver.
Leo Liberti obtained his Ph.D. in Global Optimization at Imperial College London, held postdoctoral fellowships at Politecnico di Milano and Ecole Polytechnique in France, where he became a professor and vice-president of his department. After two years as a Research Staff Member at IBM Research in New York, he moved back to Europe as a Research Director at CNRS and part-time professor at Ecole Polytechnique. His main research interests are mixed-integer nonlinear programming and distance geometry.