Branching and bounds tighteningtechniques for non-convex MINLP

By Pietro Belotti, Jon Lee, Leo Liberti, François Margot, Andreas Wächter. Optim. Methods Softw., 2009

704 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/b5d9a8c73fe268edffe1f4511d34b489e7b5f58a

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Citations in the corpus

GloMIQO: Global mixed-integer quadratic optimizer (2012, methodology): “…111 InterestingbranchingstrategiessuitableforMIQCQPincludesimpleheuristicstrategies fordeterminingthevariablewiththegreatestassociatederror[6,7,18],strongbranching [2],violationtransfer[133,134],andreliabilitybranching[2,27].”
Distance geometry and data science (2019, background): “zes them, and then relaxes the dening constraints. Carrying this out recursively for every term in an NLP [132], and only relaxing the nonlinear dening constraints yields an LP relaxation of an NLP [169, 172, 23]. 3 Distance Geometry DG refers to a foundation of geometry based on the concept of dist”
Multiphase Mixed-Integer Optimal Control Approach to Aircraft Trajectory Optimization (2013, methodology): “Although systematic methods exist to compute convex approximations for such nonlinear equations (for example, within the solvers Baron [20,21] and Couenne [22]), their efficiency is limited.”
Systemic risk-efficient asset allocations: Minimization of systemic risk as a network optimization problem (2018, methodology): “In the following we show the results from the Couenne solver, which provides the minimal objective values.”
A review and comparison of solvers for convex MINLP (2018, methodology): “The solver implements an LB based spatial branch and bound technique as its main algorithm, in addition to bound reduction techniques and primal heuristics [8].”
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].”
On handling indicator constraints in mixed integer programming (2016, methodology): “Probing is a common tightening technique in MIP and MINLP solvers (see [28], and [3] and [30], respectively.”
Mixed-integer nonlinear optimization*† (2013, methodology): “The performance of the BB algorithm depends strongly on the choice of i and b (Belotti et al., 2009; Tawarmalani and Sahinidis, 2002).”
On the Computational Studies of Deterministic Global Optimization of Head Dependent Short-Term Hydro Scheduling (2013, methodology): “This is currently an active area of research in which there are available several solvers, such as BARON [31], LINDOGlobal [32], and Couenne [33], which can address the deterministic global solution of NLP and MINLP problems.”
Non-convex mixed-integer nonlinear programming: A survey (2012, background): “Some further enhanced rules for domain reduction, branching variable selection and branching value have also been given by Belotti et al. [15].”
MINLP Solver Software (2011, background): “Couenne (Convex Over and Under ENvelopes for Nonlinear Estimation) [9].”