Linearization and parallelization schemes for convex mixed-integer nonlinear optimization

Meenarli Sharma (), Prashant Palkar () and Ashutosh Mahajan ()
Additional contact information
Meenarli Sharma: Indian Institute of Technology Bombay
Prashant Palkar: Indian Institute of Technology Bombay
Ashutosh Mahajan: Indian Institute of Technology Bombay

Computational Optimization and Applications, 2022, vol. 81, issue 2, No 4, 423-478

Abstract: Abstract 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.

Keywords: Convex MINLP; Linearization techniques; Branch-and-bound; Outer approximation; Shared-memory parallel (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10589-021-00335-x Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:coopap:v:81:y:2022:i:2:d:10.1007_s10589-021-00335-x

Ordering information: This journal article can be ordered from
http://www.springer.com/math/journal/10589

DOI: 10.1007/s10589-021-00335-x

Access Statistics for this article

Computational Optimization and Applications is currently edited by William W. Hager

More articles in Computational Optimization and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().