Polyhedral approximation strategies for nonconvex mixed-integer nonlinear programming in SHOT

Abstract Different versions of polyhedral outer approximation are used by many algorithms for mixed-integer nonlinear programming (MINLP). While it has been demonstrated that such methods work well convex MINLP, extending them to solve nonconvex problems traditionally challenging. The Supporting Hyperplane Optimization Toolkit (SHOT) is a solver based on approximations the feasible set MINLP problems. SHOT an open source COIN-OR project, and currently one most efficient global solvers MINLP. In this paper, we discuss some extensions significantly extend its applicability functionality include utilizing convexity detection selecting nonlinearities linearize, lifting reformulations special classes functions, feasibility relaxations infeasible subproblems adding objective cuts force search better solutions. This not unique SHOT, but can be implemented in other similar as well. addition discussing new extensive benchmark deterministic performed provides snapshot current state