Immanuel M. Bomze

New results for molecular formation under pairwise potential minimization

Categories Global Optimization, Global Optimization Applications, Global Optimization Theory Tags , , , , ,

We establish new lower bounds on the distance between two points of a minimum energy configuration of $N$ points in $\mathbb{R}^3$ interacting according to a pairwise potential function. For the Lennard-Jones case, this bound is 0.67985 (and 0.7633 in the planar case). A similar argument yields an estimate for the minimal distance in Morse clusters, … Read more

Solving standard quadratic optimization problems via linear, semidefinite and copositive programming

Categories Combinatorial Optimization, Global Optimization Theory, Semi-definite Programming Tags , , , ,

The problem of minimizing a (non-convex) quadratic function over the simplex (the standard quadratic optimization problem) has an exact convex reformulation as a copositive programming problem. In this paper we show how to approximate the optimal solution by approximating the cone of copositive matrices via systems of linear inequalities, and, more refined, linear matrix inequalities … Read more