Linearization and parallelization schemes for convex mixed-integer nonlinear optimization

We develop and test linearization and parallelization schemes for convex mixed-integer nonlinear programming. Several linearization approaches are proposed for LP/NLP based branch-and-bound. Some of these approaches strengthen the linear approximation to nonlinear constraints at the root node and so...

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Bibliographic Details
Published in:Computational optimization and applications Vol. 81; no. 2; pp. 423 - 478
Main Authors: Sharma, Meenarli, Palkar, Prashant, Mahajan, Ashutosh
Format: Journal Article
Language:English
Published: New York Springer US 01.03.2022
Springer Nature B.V
Subjects:
Algorithms
Approximation
Convex and Discrete Geometry
Linearization
Management Science
Mathematics
Mathematics and Statistics
Mixed integer
Nodes
Nonlinear programming
Operations Research
Operations Research/Decision Theory
Optimization
Statistics
Toolkits
Variables
Branch-and-bound
Convex MINLP
Outer approximation
Linearization techniques
Shared-memory parallel
ISSN:0926-6003, 1573-2894
Online Access:Get full text
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Summary:We develop and test linearization and parallelization schemes for convex mixed-integer nonlinear programming. Several linearization approaches are proposed for LP/NLP based branch-and-bound. Some of these approaches strengthen the linear approximation to nonlinear constraints at the root node and some at the other branch-and-bound nodes. Two of the techniques are specifically applicable to commonly found univariate nonlinear functions and are more effective than other general approaches. These techniques have been implemented in the Minotaur toolkit. Tests on benchmark instances show up to 12% improvement in the average time to solve the instances. Shared-memory parallel versions of NLP based branch-and-bound and LP/NLP based branch-and-bound algorithms have also been developed in the toolkit. These implementations solve different nodes of branch-and-bound concurrently. About 44% improvement in the speed and an increase in the number of instances solved within the time limit are observed when the two schemes are used together on a computer with 16 cores. These parallelization methods are compared to alternate approaches that exploit parallelism in existing commercial MILP solvers. The latter approaches are seen to perform better thus highlighting the importance of MILP techniques.
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ISSN:0926-6003
1573-2894
DOI:10.1007/s10589-021-00335-x