A branch and cut algorithm for nonconvex quadratically constrained quadratic programming

Audet, Charles; Hansen, Pierre; Jaumard, Brigitte; Savard, Gilles

doi:10.1007/s101079900106

Cited by 145 publications

(127 citation statements)

References 29 publications

Supporting

Mentioning

127

Contrasting

Order By: Relevance

“…In addition to relaxing bilinear terms using the convex hull, the BARON preprocessing routines detect connected multivariable terms within quadratic equations [26]. -Branch-and-cut for QCQP [18,19,20,21] Audet et al [18] discuss their implementation of a branch-and-cut global optimization algorithm for QCQP which made contributions to generating cutting planes and boundupdating strategies. -Couenne [27,88] Like αBB and BARON, Couenne addresses generic MINLP to ε-global optimality and relaxes bilinear terms using the convex hull.…”

Section: Literature Reviewmentioning

confidence: 99%

“…These products are additionally useful in the context of variable bounding [18,127,128]. Because there may be many possible RLT equations in MIQCQP, multiple filtering techniques exist to automatically reduce the size of the RLT representation [124,127,128].…”

Section: Literature Reviewmentioning

confidence: 99%

“…Interesting branching strategies suitable for MIQCQP include simple heuristic strategies for determining the variable with the greatest associated error [6,7,18], strong branching [2], violation transfer [133,134], and reliability branching [2,27]. GloMIQO uses reliability branching, a technique that integrates strong branching with a pseudocost heuristic to predict the best branching variable [2,27].…”

Section: Literature Reviewmentioning

confidence: 99%

“…Variable bounding algorithms relevant to this work include: interval arithmetic bounds tightening [6,7,15,18,27,127,128], optimality-based bounds tightening [89,133], reduced cost bounds tightening [117,118], and quadratic equation constraint satisfaction [44,45,77].…”

Section: Literature Reviewmentioning

confidence: 99%

See 3 more Smart Citations

GloMIQO: Global mixed-integer quadratic optimizer

2012

View full text Add to dashboard Cite

This paper introduces the Global Mixed-Integer Quadratic Optimizer, GloMIQO, a numerical solver addressing mixed-integer quadratically-constrained quadratic programs (MIQCQP) to ε-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,

show abstract

Section: Literature Reviewmentioning

confidence: 99%

Section: Literature Reviewmentioning

confidence: 99%

Section: Literature Reviewmentioning

confidence: 99%

Section: Literature Reviewmentioning

confidence: 99%

See 2 more Smart Citations

GloMIQO: Global mixed-integer quadratic optimizer

2012

View full text Add to dashboard Cite

show abstract

“…In [2], nonconvex subproblems were also handled quite efficiently by using other computational techniques. In the nonconvex case, one might also use [1,4] for solving the subproblems.…”

Section: Sequential Quadratically Constrained Quadratic Programmingmentioning

confidence: 99%

Inexact Josephy–Newton framework for generalized equations and its applications to local analysis of Newtonian methods for constrained optimization

Izmailov

Solodov

2009

Comput Optim Appl

View full text Add to dashboard Cite

We propose and analyze a perturbed version of the classical JosephyNewton method for solving generalized equations. This perturbed framework is convenient to treat in a unified way standard sequential quadratic programming, its stabilized version, sequential quadratically constrained quadratic programming, and linearly constrained Lagrangian methods. For the linearly constrained Lagrangian methods, in particular, we obtain superlinear convergence under the second-order sufficient optimality condition and the strict Mangasarian-Fromovitz constraint qualification, while previous results in the literature assume (in addition to second-order sufficiency) the stronger linear independence constraint qualification as well as the strict complementarity condition. For the sequential quadratically constrained quadratic programming methods, we prove primal-dual superlinear/quadratic convergence under the same assumptions as above, which also gives a new result.

show abstract