## Mixed Integer Nonlinear ProgrammingMany engineering, operations, and scientific applications include a mixture of discrete and continuous decision variables and nonlinear relationships involving the decision variables that have a pronounced effect on the set of feasible and optimal solutions. Mixed-integer nonlinear programming (MINLP) problems combine the numerical difficulties of handling nonlinear functions with the challenge of optimizing in the context of nonconvex functions and discrete variables. MINLP is one of the most flexible modeling paradigms available for optimization; but because its scope is so broad, in the most general cases it is hopelessly intractable. Nonetheless, an expanding body of researchers and practitioners — including chemical engineers, operations researchers, industrial engineers, mechanical engineers, economists, statisticians, computer scientists, operations managers, and mathematical programmers — are interested in solving large-scale MINLP instances. |

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### Contents

Disjunctive Programming | 90 |

Nonlinear Programming | 145 |

Expression Graphs | 244 |

Convexification and Linearization | 284 |

MixedInteger Quadraticaly Constrained Optimization | 372 |

Combinatorial Optimization | 446 |

Complexity | 532 |

Applications | 594 |

IMA HOT TOPICS WORKSHOP PARTICIPANTS | 671 |

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### Common terms and phrases

algebraic algorithm Applications approach BONMIN branch-and-bound branching breakpoints columns combinatorial combinatorial optimization computational cone convergence convex combination convex function convex hull convex MINLP CPLEX cutting plane defined denote discrete disjunctive cuts dual Editors equations facility feasible region feasible solution finite fixed formulation given global optimization Graver basis Grossmann inequalities infeasible instances Integer Nonlinear Programming integer variables interior-point method iteration Lagrangian Lemma Leyffer linear programming lower bound LP relaxation Math Mathematical Programming matrix MILP minimizer MIQCP Mixed Integer Nonlinear node nonconvex nonlinear programming NP-hard objective function obtained optimal solution optimization problems outer approximation piecewise linear polynomial polytope primal-dual product program QP subproblem quadratic programming reformulation satisfies Section semidefinite programming SIAM signomial solver solving Springer Science+Business Media SQP methods symmetry Table techniques Theorem tion upper bound vector