Integrating SQP and BranchandBound for Mixed Integer Nonlinear Programming
 Sven Leyffer
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Abstract
This paper considers the solution of Mixed Integer Nonlinear Programming (MINLP) problems. Classical methods for the solution of MINLP problems decompose the problem by separating the nonlinear part from the integer part. This approach is largely due to the existence of packaged software for solving Nonlinear Programming (NLP) and Mixed Integer Linear Programming problems.
In contrast, an integrated approach to solving MINLP problems is considered here. This new algorithm is based on branchandbound, but does not require the NLP problem at each node to be solved to optimality. Instead, branching is allowed after each iteration of the NLP solver. In this way, the nonlinear part of the MINLP problem is solved whilst searching the tree. The nonlinear solver that is considered in this paper is a Sequential Quadratic Programming solver.
A numerical comparison of the new method with nonlinear branchandbound is presented and a factor of up to 3 improvement over branchandbound is observed.
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 Title
 Integrating SQP and BranchandBound for Mixed Integer Nonlinear Programming
 Journal

Computational Optimization and Applications
Volume 18, Issue 3 , pp 295309
 Cover Date
 20010301
 DOI
 10.1023/A:1011241421041
 Print ISSN
 09266003
 Online ISSN
 15732894
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 mixed integer nonlinear programming
 branchandbound
 sequential quadratic programming
 Industry Sectors
 Authors

 Sven Leyffer ^{(1)}
 Author Affiliations

 1. Department of Mathematics, University of Dundee, Dundee, U.K.