# Convex quadratic underestimation and Branch and Bound for univariate global optimization with one nonconvex constraint

RAIRO - Operations Research (2006)

- Volume: 40, Issue: 3, page 285-302
- ISSN: 0399-0559

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topLe Thi, Hoai An, and Ouanes, Mohand. "Convex quadratic underestimation and Branch and Bound for univariate global optimization with one nonconvex constraint." RAIRO - Operations Research 40.3 (2006): 285-302. <http://eudml.org/doc/249771>.

@article{LeThi2006,

abstract = {
The purpose of this paper is to demonstrate that, for globally minimize one dimensional nonconvex problems with
both twice differentiable function and constraint, we can propose an efficient
algorithm based on Branch and Bound techniques. The method is first
displayed in the simple case with an interval constraint. The extension is
displayed
afterwards to the general case with an additional nonconvex twice
differentiable constraint. A quadratic bounding function which is better
than the well known linear underestimator is proposed while w-subdivision
is added to support the branching procedure. Computational results on several and
various types of functions show the efficiency of our algorithms and their
superiority with respect to the existing methods.
},

author = {Le Thi, Hoai An, Ouanes, Mohand},

journal = {RAIRO - Operations Research},

keywords = {Global optimization; branch and bound; quadratic underestimation; w-subdivision.; global optimization; quadratic underestimation; -subdivision},

language = {eng},

month = {11},

number = {3},

pages = {285-302},

publisher = {EDP Sciences},

title = {Convex quadratic underestimation and Branch and Bound for univariate global optimization with one nonconvex constraint},

url = {http://eudml.org/doc/249771},

volume = {40},

year = {2006},

}

TY - JOUR

AU - Le Thi, Hoai An

AU - Ouanes, Mohand

TI - Convex quadratic underestimation and Branch and Bound for univariate global optimization with one nonconvex constraint

JO - RAIRO - Operations Research

DA - 2006/11//

PB - EDP Sciences

VL - 40

IS - 3

SP - 285

EP - 302

AB -
The purpose of this paper is to demonstrate that, for globally minimize one dimensional nonconvex problems with
both twice differentiable function and constraint, we can propose an efficient
algorithm based on Branch and Bound techniques. The method is first
displayed in the simple case with an interval constraint. The extension is
displayed
afterwards to the general case with an additional nonconvex twice
differentiable constraint. A quadratic bounding function which is better
than the well known linear underestimator is proposed while w-subdivision
is added to support the branching procedure. Computational results on several and
various types of functions show the efficiency of our algorithms and their
superiority with respect to the existing methods.

LA - eng

KW - Global optimization; branch and bound; quadratic underestimation; w-subdivision.; global optimization; quadratic underestimation; -subdivision

UR - http://eudml.org/doc/249771

ER -

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