Disjunctive cuts in Mixed-Integer Conic Optimization

This paper studies disjunctive cutting planes in Mixed-Integer Conic Programming. Building on conic duality, we formulate a cut-generating program for separating cuts, and investigate the impact of normalization condition its resolution. In particular, show that careful selection guarantees solvability strong duality. Then, highlight shortcomings conic-infeasible points an outer-approximation context, propose extensions to classical lifting monoidal strengthening procedures. Finally, assess computational behavior various conditions terms gap closed, computing time cut sparsity. process, our approach is competitive with internal lift-and-project cuts state-of-the-art solver.