Mixed Integer Nonlinear Programming

Many 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.

Many 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.

​Foreword.- Preface.-Algorithms and software for convex mixed integer nonlinearprograms.-  Subgradient based outer approximation for mixed integer secondorder cone programming.-Perspective reformulation and applications.- Generalized disjunctive programming: A framework for formulation and alternative algorithms for MINLP optimization.-Disjunctive cuts for nonconvex MINLP.- Sequential quadratic programming methods.- Using interior-point methods within an outer approximation framework for mixed integer nonlinear programming.- Using expression graphs in optimization algorithms.- Symmetry in mathematical programming.- Using piecewise linear functions for solving MINLPs.- An algorithmic framework for MINLP with separable non-convexity.- Global optimization of mixed-integer signomial programming problems.-The MILP road to MIQCP.- Linear programming relaxations of quadratically constrained quadratic programs.- Extending a CIP framework to solve MIQCPs.- Computation with polynomial equations and inequalities arisingin combinatorial optimization.-  Matrix relaxations in combinatorial optimization.- A polytope for a product of real linear functions in 0/1 variables.- On the complexity of nonlinear mixed-integer optimization.- Theory and applications of n-fold integer programming.- MINLP Application for ACH interiors restructuring.- A benchmark library of mixed-integer optimal control problems.