SHOT swMATH ID: 15630 Software Authors: Kronqvist, Jan; Lundell, Andreas; Westerlund, Tapio Description: The extended supporting hyperplane algorithm for convex mixed-integer nonlinear programming. A new deterministic algorithm for solving convex mixed-integer nonlinear programming (MINLP) problems is presented in this paper: The extended supporting hyperplane (ESH) algorithm uses supporting hyperplanes to generate a tight overestimated polyhedral set of the feasible set defined by linear and nonlinear constraints. A sequence of linear or quadratic integer-relaxed subproblems are first solved to rapidly generate a tight linear relaxation of the original MINLP problem. After an initial overestimated set has been obtained the algorithm solves a sequence of mixed-integer linear programming or mixed-integer quadratic programming subproblems and refines the overestimated set by generating more supporting hyperplanes in each iteration. Compared to the extended cutting plane algorithm ESH generates a tighter overestimated set and unlike outer approximation the generation point for the supporting hyperplanes is found by a simple line search procedure. In this paper it is proven that the ESH algorithm converges to a global optimum for convex MINLP problems. The ESH algorithm is implemented as the supporting hyperplane optimization toolkit (SHOT) solver, and an extensive numerical comparison of its performance against other state-of-the-art MINLP solvers is presented. Homepage: http://link.springer.com/article/10.1007/s10898-015-0322-3 Keywords: convex mixed integer nonlinear programming; extended supporting hyperplane algorithm; extended cutting plane algorithm; supporting hyperplanes; cutting planes; supporting hyperplane optimization toolkit Related Software: Ipopt; MINLPLib; Bonmin; SCIP; MINLP; ANTIGONE; Pyomo; Gurobi; Decogo; AlphaECP; FEASPUMP; CPLEX; Muriqui; LINDO; LINDOGlobal; BARON; MINOTAUR; DICOPT; PAVER; FilMINT Cited in: 27 Documents Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year The extended supporting hyperplane algorithm for convex mixed-integer nonlinear programming. Zbl 1339.90247Kronqvist, Jan; Lundell, Andreas; Westerlund, Tapio 2016 all top 5 Cited by 46 Authors 7 Kronqvist, Jan 5 Westerlund, Tapio 4 Lundell, Andreas 3 Hendrix, Eligius M. T. 3 Muts, Pavlo 3 Nowak, Ivo 2 Bernal, David E. 2 Eronen, Ville-Pekka 2 Fampa, Marcia Helena C. 2 Grossmann, Ignacio E. 2 Mäkelä, Marko Mikael 2 Melo, Wendel A. X. 2 Misener, Ruth 2 Raupp, Fernanda M. P. 1 Allman, Andrew 1 Berthold, Timo 1 Davarnia, Danial 1 De Mauri, Massimo 1 Dörfler, Daniel 1 Gillis, Joris J. M. 1 Gleixner, Ambros M. 1 Krennrich, Gerhard 1 Le Thi, Hoai An 1 Lee, Robert M. 1 Letsios, Dimitrios 1 Mistry, Miten 1 Müller, Sven-André 1 Neumann, Christoph 1 Palkar, Prashant 1 Peng, Zedong 1 Pham Dinh Tao 1 Pipeleers, Goele 1 Roemer, Nils 1 Santos, Haroldo Gambini 1 Schwarz, Robert 1 Sergeev, Yaroslav Dmitrievich 1 Serra, Thiago R. 1 Serrano, Felipe 1 Sharma, Meenarli 1 Souza Brito, Samuel 1 Stein, Oliver 1 Swevers, Jan 1 van Hoeve, Willem-Jan 1 Voigt, Guido 1 Witzig, Jakob 1 Zhang, Qi all top 5 Cited in 11 Serials 10 Journal of Global Optimization 3 Annals of Operations Research 2 Mathematical Programming. Series A. Series B 2 Computational Optimization and Applications 2 INFORMS Journal on Computing 2 Optimization and Engineering 1 Journal of Optimization Theory and Applications 1 Optimization 1 Computers & Operations Research 1 European Journal of Operational Research 1 SIAM Journal on Optimization Cited in 5 Fields 27 Operations research, mathematical programming (90-XX) 2 Numerical analysis (65-XX) 1 General and overarching topics; collections (00-XX) 1 Convex and discrete geometry (52-XX) 1 Statistics (62-XX) Citations by Year