Motivated by encouraging numerical results in Eltved and Burer (2023)[13], in this note we
consider two specific variants of the trust-region subproblem and provide exact semidefinite …

We study $\mu_5 (n) $, the minimum number of convex pentagons induced by $ n $ points
in the plane in general position. Despite a significant body of research in understanding …

We develop a new method called affine FR for recovering Slater's condition for semidefinite
programming (SDP) relaxations of combinatorial optimization (CO) problems. Affine FR is a …

Motivated by encouraging numerical results in [13], in this note we consider two specific
variants of the trust-region subproblem and provide exact semidefinite representable …

In general, convex programs have nicer properties than nonconvex programs. Notably, in a
convex program, every locally optimal solution is also globally optimal. For this reason, there …

We propose a special facial reduction algorithm (FRA) for the Shor semidefinite
programming (SDP) relaxation of the quadratically constrained quadratic program (QCQP) …

We develop a new method called affine FR for recovering Slater's condition for semidefinite
8 programming (SDP) relaxations of combinatorial optimization (CO) problems. Affine FR is …