Two linear approximation algorithms for convex mixed integer nonlinear programming

Wendel Melo (), Marcia Fampa () and Fernanda Raupp ()
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Wendel Melo: Federal University of Uberlandia
Marcia Fampa: Federal University of Rio de Janeiro
Fernanda Raupp: National Laboratory for Scientific Computing of the Ministry of Science, Technology, Innovations and Communications

Annals of Operations Research, 2022, vol. 316, issue 2, No 33, 1491 pages

Abstract: Abstract We present two new algorithms for convex Mixed Integer Nonlinear Programming (MINLP), both based on the well known Extended Cutting Plane (ECP) algorithm proposed by Weterlund and Petersson. Our first algorithm, Refined Extended Cutting Plane (RECP), incorporates additional cuts to the MILP relaxation of the original problem, obtained by solving linear relaxations of NLP problems considered in the Outer Approximation algorithm. Our second algorithm, Linear Programming based Branch-and-Bound (LP-BB), applies the strategy of generating cuts that is used in RECP, to the linear approximation scheme used by the LP/NLP based Branch-and-Bound algorithm. Our computational results show that RECP and LP-BB are highly competitive with the most popular MINLP algorithms from the literature, while keeping the nice and desirable characteristic of ECP, of being a first-order method.

Keywords: Mixed integer nonlinear programming; Extended cutting plane; Outer approximation; Linear approximation (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10479-020-03722-5

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