Disjunctive cuts in Mixed-Integer Conic Optimization

TL;DR

This paper advances disjunctive cutting planes in Mixed-Integer Conic Programming by formulating a new cut-generating conic program, analyzing normalization impacts, and proposing extensions to classical procedures, with competitive computational results.

Contribution

It introduces a novel conic formulation for disjunctive cuts, explores normalization effects on solvability, and extends classical lifting and strengthening methods for improved cutting-plane generation.

Findings

Normalization guarantees solvability and strong duality.

Conic extensions improve classical lifting and strengthening procedures.

Approach is competitive with state-of-the-art solver cuts.

Abstract

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