The supporting hyperplane optimization toolkit for convex MINLP

Abstract In this paper, an open-source solver for mixed-integer nonlinear programming (MINLP) problems is presented. The Supporting Hyperplane Optimization Toolkit (SHOT) combines a dual strategy based on polyhedral outer approximations (POA) with primal heuristics. POA achieved by expressing the feasible set of MINLP problem linearizations obtained extended supporting hyperplane (ESH) and cutting plane (ECP) algorithms. can be tightly integrated (MIP) subsolver in so-called single-tree manner, i.e. , only single MIP optimization solved, where are added as lazy constraints through callbacks solver. This enables to reuse branching tree each iteration, contrast most other POA-based methods. SHOT available COIN-OR project, it utilizes flexible task-based structure making easy extend modify. It currently GAMS, utilized AMPL, Pyomo JuMP well its ASL interface. main functionality solution strategies implemented described their impact performance illustrated numerical benchmarks 406 convex from MINLPLib library. Many features introduced solvers well. To show overall effectiveness SHOT, also compared state-of-the-art same benchmark set.