Ebook: 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.

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?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.

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?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.
Content:
Front Matter....Pages i-xvii
Front Matter....Pages 1-1
Algorithms and Software for Convex Mixed Integer Nonlinear Programs....Pages 1-39
Subgradient Based Outer Approximation for Mixed Integer Second Order Cone Programming....Pages 41-59
Perspective Reformulation and Applications....Pages 61-89
Front Matter....Pages 91-91
Generalized Disjunctive Programming: A Framework for Formulation and Alternative Algorithms for MINLP Optimization....Pages 93-115
Disjunctive Cuts for Nonconvex MINLP....Pages 117-144
Front Matter....Pages 145-145
Sequential Quadratic Programming Methods....Pages 147-224
Using Interior-Point Methods within an Outer Approximation Framework for Mixed Integer Nonlinear Programming....Pages 225-243
Front Matter....Pages 245-245
Using Expression Graphs in Optimization Algorithms....Pages 247-262
Symmetry in Mathematical Programming....Pages 263-283
Front Matter....Pages 285-285
An Algorithmic Framework for MINLP with Separable Non-Convexity....Pages 287-314
Global Optimization of Mixed-Integer Signomial Programming Problems....Pages 315-347
Front Matter....Pages 349-369
The MILP Road to MIQCP....Pages 371-371
Linear Programming Relaxations of Quadratically Constrained Quadratic Programs....Pages 373-405
Front Matter....Pages 407-426
Computation with Polynomial Equations and Inequalities Arising in Combinatorial Optimization....Pages 427-444
Matrix Relaxations in Combinatorial Optimization....Pages 445-445
A Polytope for a Product of Real Linear Functions in 0/1 Variables....Pages 447-481
Front Matter....Pages 483-511
On the Complexity of Nonlinear Mixed-Integer Optimization....Pages 513-529
Theory and Applications of n-Fold Integer Programming....Pages 531-531
Front Matter....Pages 533-557
MINLP Application for ACH Interiors Restructuring....Pages 559-593
A Benchmark Library of Mixed-Integer Optimal Control Problems....Pages 595-595
Back Matter....Pages 597-629
....Pages 631-670