Two linear approximation algorithms for convex mixed integer nonlinear programming

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 relaxati...

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Bibliographic Details
Published in:Annals of operations research Vol. 316; no. 2; pp. 1471 - 1491
Main Authors: Melo, Wendel, Fampa, Marcia, Raupp, Fernanda
Format: Journal Article
Language:English
Published: New York Springer US 01.09.2022
Springer
Springer Nature B.V
Subjects:
Algorithms
Approximation
Business and Management
Combinatorics
Cutting
Linear programming
Management research
Mathematical analysis
Mixed integer
Nonlinear programming
Operations research
Operations Research/Decision Theory
S.i.: Claio 2018
Theory of Computation
Brazil
Mixed integer nonlinear programming
Outer approximation
Linear approximation
Extended cutting plane
ISSN:0254-5330, 1572-9338
Online Access:Get full text
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Summary: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.
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ISSN:0254-5330
1572-9338
DOI:10.1007/s10479-020-03722-5