Global optimization of mixed-integer nonlinear programs: A theoretical and computational study

By Mohit Tawarmalani, Nikolaos V. Sahinidis. Mathematical programming, 2004

619 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Control and Systems Engineering, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/404913b06f30abc44ab9b2d4f17f0cd18267dc84

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Citations in the corpus

Copositive Programming – a Survey (2010, methodology): “However, the method turns out to be very successful for the standard quadratic problem: while a standard global optimization solver like BARON [55] solves StQPs in 30 variables in about 1000 seconds, this method solves problems in 2000 variables in 30 seconds (on average).”
Mixed-integer nonlinear optimization*† (2013, background): “The approach of reducing multivariate functions to univariate functions has a few potential disadvantages, which have been pointed out, for example, by Tomlin (1981); Lee and Wilson (2001) and Vielma et al.”
Verification methods: rigorous results using floating-point arithmetic (2010, background): “6) It was Problem 4 of the 10 × 10-digit challenge by Trefethen (2002) to compute the global minimum of this function over R2.”
State-Of-The-Art Review of Mathematical Optimisation Approaches for Synthesis of Energy Systems (2017, methodology): “This algorithm uses branch-and-bound like techniques to decompose large and complexMINLP problems into a set of smaller sub-problems (Misener et al. 2009; Tawarmalani and Sahinidis 2004).”
GloMIQO: Global mixed-integer quadratic optimizer (2012, neutral): “…111 InterestingbranchingstrategiessuitableforMIQCQPincludesimpleheuristicstrategies fordeterminingthevariablewiththegreatestassociatederror[6,7,18],strongbranching [2],violationtransfer[133,134],andreliabilitybranching[2,27].”
A polyhedral branch-and-cut approach to global optimization (2005, methodology): “The idea to construct and solve entirely polyhedral-based relaxations in the context of branch-and-bound for global optimization was first proposed and analyzed by Tawarmalani and Sahinidis in [21], where polyhedral outer approximations of univariate convex functions and bivariate functions were inc”
Branching and bounds tighteningtechniques for non-convex MINLP (2009, methodology): “This strategy is similar to the one described by Tawarmalani and Sahinidis [79, page 194].”
Set-Theoretic Approaches in Analysis, Estimation and Control of Nonlinear Systems (2015, methodology): “Other approaches to convex/polyhedral enclosures include the decomposition/relaxation/outerapproximation technique (Smith and Pantelides, 1999; Tawarmalani and Sahinidis, 2004) as well as McCormick’s relaxation technique (McCormick, 1976; Mitsos et al.”
Distance geometry and data science (2019, methodology): “Carrying this out recursively for every term in an NLP (McCormick 1976) and only relaxing the nonlinear defining constraints yield an LP relaxation of an NLP (Smith and Pantelides 1999; Tawarmalani and Sahinidis 2004; Belotti et al.”
A review of recent advances in global optimization (2009, background): “Tawarmalani and Sahinidis (2004) developed a branch and bound framework for the global optimization of continuous, integer, and mixed-integer nonlinear programs.”
ANTIGONE: Algorithms for coNTinuous / Integer Global Optimization of Nonlinear Equations (2014, methodology): “For more complex terms, ANTIGONE introduces auxiliary variables [16, 57, 130, 136–138, 145]; this strategy is in contrast to systems exclusively using underestimators that do not introduce auxiliary variables [4, 5, 92, 95, 108].”
MINLP Solver Software (2011, methodology): “In this category we have alphaBB, AlphaECP, AOA, BARON, DICOPT, LaGO, and LindoGlobal.”
Non-convex mixed-integer nonlinear programming: A survey (2012, background): “In [59], a unified framework is given for domain reduction strategies, and, in [60], it is shown that, even when a constraint is convex, it may be helpful (in terms of tightness of the resulting relaxation) to introduce additional variables and split the constraint into two constraints.”
Complete search in continuous global optimization and constraint satisfaction (2004, methodology): “(3) Tsuda and Kiono (1964) introduced the Monte Carlo method for finding solutions of systems of equations; and the thesis by Mockus (1966) applied it to global optimization.”
Review of Nonlinear Mixed-Integer and Disjunctive Programming Techniques (2002, methodology): “Examples of global optimization methods for MINLP problems include the branch and reduce method by Ryoo and Sahinidis (1995) and Tawarmalani and Sahinidis (2000), the α-BB method by Adjiman et al (2000), the reformulation/spatial branch and bound search method by Smith and Pantelides (1999), the…”