A polyhedral branch-and-cut approach to global optimization

By Mohit Tawarmalani, Nikolaos V. Sahinidis. Mathematical programming, 2005

1,352 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/60162e794d1de72c08336d5ad89122522fc91902

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Citations in the corpus

Near-Field Communications: A Tutorial Review (2023, methodology): “The branch-and-bound (BnB) algorithm [71] can be used to obtain the globally optimal solution of MINLP problems, but has exponential complexity.”
GloMIQO: Global mixed-integer quadratic optimizer (2012, methodology): “To test the performance of the solver GloMIQO, we compared the 399 test problems outlined in Table 2 against the state-of-the-art global optimization solvers listed in Table 1: BARON 10.1.2 [ 135], Couenne 0.4 [27], LindoGLOBAL 6.1.1.588 [ 63,87], and SCIP 2.1.0 [2,3,30,31].”
A disjunctive convex programming approach to the pollution-routing problem (2016, methodology): “It can be solved by MICP solvers such as Bonmin [15], DICOPT [32], and FilMINT [1], or solved as a mixed integer nonlinear program (MINLP) by global optimization solvers such as Antigone [50], Baron [56], MINOTAUR [47], and SCIP [2].”
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.”
Inexactness of SDP Relaxation and Valid Inequalities for Optimal Power Flow (2014, methodology): “We should note that the global solver BARON can be computationally expensive.”
Learning surrogate models for simulation‐based optimization (2014, methodology): “The red line shows the pareto curve generated by solving a nonconvex nonlinear weighted objective function problem using BARON.”
ANTIGONE: Algorithms for coNTinuous / Integer Global Optimization of Nonlinear Equations (2014, neutral): “3 [139], Couenne 0.4 [17], LINDO 8 .”
Derivative-free optimization: a review of algorithms and comparison of software implementations (2012, methodology): “BARON's branch-and-bound strategy was able to guarantee global optimality for most of the test problems, although this solver does not accept trigonometric and some other nonlinear functions.”
Branching and bounds tighteningtechniques for non-convex MINLP (2009, methodology): “Branch-and-Bound methods that generate lower bounds using both reformulation and the convexity of a subset of constraints have also been developed [83].”
Stochastic pooling problem for natural gas production network design and operation under uncertainty (2011, background): “MINLP problems are typically solved with BB strategies, such as branchand-reduce,44 SMIN-aBB, and GMIN-aBB,45 or decomposition strategies, such as outer approximation,46–48 and GBD.49 A detailed survey of MINLP solution techniques can be found in the review article by Grossmann.50”
Convex Hull of the Quadratic Branch AC Power Flow Equations and Its Application in Radial Distribution Networks (2017, methodology): “Based on the BFM in radial networks, reference [11] proposes a set of non-iterative linear cuts to obtain a tight root node for solving the OPF problem in BARON [12]; valid linear cuts are generated iteratively for tightening the SOCP relaxation of OPFs in [13]; Several convex constraints which can ”
A review of recent advances in global optimization (2009, background): “Tawarmalani and Sahinidis (2005) introduced a polyhedral branch-and-cut approach in global optimization.”
Strong SOCP Relaxations for the Optimal Power Flow Problem (2015, positive): “bjective RM AM A∗ SOCP 9-bus quadratic 89.46 69.13 52.69 Here, the percentage optimality gap is calculated as 100 × z*−zLB z* , where z* is the global optimal objective function value found by BARON (Tawarmalani and Sahinidis 2005) and zLB is the optimal objective cost of a particular relaxation. 2.”