SHOT
swMATH ID:  15630 
Software Authors:  Kronqvist, Jan; Lundell, Andreas; Westerlund, Tapio 
Description:  The extended supporting hyperplane algorithm for convex mixedinteger nonlinear programming. A new deterministic algorithm for solving convex mixedinteger 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 integerrelaxed 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 mixedinteger linear programming or mixedinteger 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 stateoftheart MINLP solvers is presented. 
Homepage:  http://link.springer.com/article/10.1007/s1089801503223 
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; ANTIGONE; SCIP; Decogo; AlphaECP; Pyomo; MINLP; LINDO; BARON; Muriqui; MINOTAUR; DICOPT; FEASPUMP; Gurobi; LINDOGlobal; Juniper; JuMP; PAVER 
Referenced in:  23 Publications 
Standard Articles
1 Publication describing the Software, including 1 Publication in zbMATH  Year 

The extended supporting hyperplane algorithm for convex mixedinteger nonlinear programming. Zbl 1339.90247 Kronqvist, Jan; Lundell, Andreas; Westerlund, Tapio 
2016

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Referenced by 41 Authors
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Referenced in 9 Serials
Referenced in 5 Fields
23  Operations research, mathematical programming (90XX) 
1  General and overarching topics; collections (00XX) 
1  Convex and discrete geometry (52XX) 
1  Statistics (62XX) 
1  Numerical analysis (65XX) 