A small polygon is a convex polygon of unit diameter. We are interested in small polygons which have the largest area for a given number of vertices n. Many instances are already solved in the literature, namely for all odd n, and for n = 4, 6 and 8. Thus, for even n ≥ 10, instances of this...

In a real situation, optimization problems often involve uncertain parameters. Robust optimization is one of distribution-free methodologies based on worst-case analyses for handling such problems. In this paper, we first focus on a special class of uncertain linear programs (LPs). Applying the...

We introduce a new relaxation framework for nonconvex quadratically constrained quadratic programs (QCQPs). In contrast to existing relaxations based on semidefinite programming (SDP), our relaxations incorporate features of both SDP and second order cone programming (SOCP) and, as a result,...