A small polygon is a polygon of unit diameter. The maximal area of a small polygon with $n=2m$ vertices is not known when $m\ge 7$. Finding the largest small $n$-gon for a given number $n\ge 3$ can be formulated as a nonconvex quadratically constrained quadratic optimization problem. We propose to solve this problem with a … Read more
In this paper, we consider the nonconvex quadratic optimization problem with a single quadratic constraint. First we give a theoretical characterization of the local non-global minimizers. Then we extend the recent characterization of the global minimizer via a generalized eigenvalue problem to the local non-global minimizers. Finally, we use these results to derive an efficient … Read more
We study approximation bounds for the SDP relaxation of quadratically constrained quadratic optimization: min f^0(x) subject to f^k(x)