Federico Battista We consider the central role of improving directions in solution methods for mixed integer bilevel linear optimization problems (MIBLPs). Current state-of-the-art methods for solving MIBLPs employ the branch-and-cut framework originally developed for solving mixed integer linear optimization problems. This approach relies on oracles for two kinds of subproblems: those for checking whether a candidate pair … Read more
The Lov\’asz theta function $\theta(G)$ provides a very good upper bound on the stability number of a graph $G$. It can be computed in polynomial time by solving a semidefinite program (SDP), which also turns out to be fairly tractable in practice. Consequently, $\theta(G)$ achieves a hard-to-beat trade-off between computational effort and strength of the … Read more
Semidefinite programs (SDPs) can be solved in polynomial time by interior point methods. However, when the dimension of the problem gets large, interior point methods become impractical in terms of both computational time and memory requirements. Certain first-order methods, such as Alternating Direction Methods of Multipliers (ADMMs), established as suitable algorithms to deal with large-scale … Read more