We present a linear cutting-plane relaxation approach that rapidly proves tight lower bounds for the Alternating Current Optimal Power Flow Problem (ACOPF). Our method leverages outer-envelope linear cuts for well-known second-order cone relaxations for ACOPF along with modern cut management techniques. These techniques prove effective on a broad family of ACOPF instances, including the largest … Read more
Diverse forms of nonlinear optimization problems can be recast to the special form of second-order cone problems (SOCPs), permitting a wider variety of highly effective solvers to be applied. Popular solvers assume, however, that the necessary transformations to required canonical forms have already been identified and carried out. We describe a general approach to the … Read more
We address combinatorial optimization problems with uncertain coefficients varying over ellipsoidal uncertainty sets. The robust counterpart of such a problem can be rewritten as a second-oder cone program (SOCP) with integrality constraints. We propose a branch-and-bound algorithm where dual bounds are computed by means of an active set algorithm. The latter is applied to the … Read more
Conic optimization is the problem of optimizing a linear function over an intersection of an affine linear manifold with the Cartesian product of convex cones. However, many real world conic models involves an intersection rather than the product of two or more cones. It is easy to deal with an intersection of one or more … Read more