Journal ArticleDOI
GloMIQO: Global mixed-integer quadratic optimizer
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TLDR
GloMIQO is introduced, a numerical solver addressing mixed-integer quadratically-constrained quadratic programs to $${\varepsilon}$$-global optimality, and its algorithmic components are presented for reformulating user input, detecting special structure including convexity and edge-concavity, generating tight convex relaxations, and finding good feasible solutions.Abstract:
This paper introduces the global mixed-integer quadratic optimizer, GloMIQO, a numerical solver addressing mixed-integer quadratically-constrained quadratic programs to $${\varepsilon}$$ -global optimality. The algorithmic components are presented for: reformulating user input, detecting special structure including convexity and edge-concavity, generating tight convex relaxations, partitioning the search space, bounding the variables, and finding good feasible solutions. To demonstrate the capacity of GloMIQO, we extensively tested its performance on a test suite of 399 problems of diverse size and structure. The test cases are taken from process networks applications, computational geometry problems, GLOBALLib, MINLPLib, and the Bonmin test set. We compare the performance of GloMIQO with respect to four state-of-the-art global optimization solvers: BARON 10.1.2, Couenne 0.4, LindoGLOBAL 6.1.1.588, and SCIP 2.1.0.read more
Citations
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I and i
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Mixed-integer nonlinear optimization
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Non-convex mixed-integer nonlinear programming: A survey
Samuel Burer,Adam N. Letchford +1 more
TL;DR: In this paper, the authors survey the literature on non-convex mixed-integer nonlinear programs, discussing applications, algorithms, and software, and special attention is paid to the case in which the objective and constraint functions are quadratic.
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ANTIGONE: Algorithms for coNTinuous / Integer Global Optimization of Nonlinear Equations
TL;DR: The purpose of this paper is to show how the extensible structure of ANTIGONE realizes the authors' previously-proposed mixed- integer quadratically-constrained quadratic program and mixed-integer signomial optimization computational frameworks.
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Scope for industrial applications of production scheduling models and solution methods
Iiro Harjunkoski,Christos T. Maravelias,Peter Bongers,Pedro M. Castro,Sebastian Engell,Ignacio E. Grossmann,John N. Hooker,Carlos A. Méndez,Guido Sand,John M. Wassick +9 more
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References
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I and i
TL;DR: There is, I think, something ethereal about i —the square root of minus one, which seems an odd beast at that time—an intruder hovering on the edge of reality.
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On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming
TL;DR: A comprehensive description of the primal-dual interior-point algorithm with a filter line-search method for nonlinear programming is provided, including the feasibility restoration phase for the filter method, second-order corrections, and inertia correction of the KKT matrix.
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Benchmarking optimization software with performance profiles
Elizabeth D. Dolan,Jorge J. Moré +1 more
TL;DR: It is shown that performance profiles combine the best features of other tools for performance evaluation to create a single tool for benchmarking and comparing optimization software.
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Lapack Users' Guide
TL;DR: The third edition of LAPACK provided a guide to troubleshooting and installation of Routines, as well as providing examples of how to convert from LINPACK or EISPACK to BLAS.
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Computability of global solutions to factorable nonconvex programs: Part I — Convex underestimating problems
TL;DR: For nonlinear programming problems which are factorable, a computable procedure for obtaining tight underestimating convex programs is presented to exclude from consideration regions where the global minimizer cannot exist.