Exact Algorithms for Global Optimization of Mixed-Integer Nonlinear Programs

2002 ◽  
pp. 65-85 ◽  
Author(s):  
Mohit Tawarmalani ◽  
Nikolaos V. Sahinidis
Keyword(s):  
Global Optimization ◽  
Exact Algorithms ◽  
Mixed Integer ◽  
Nonlinear Programs

scholarly journals Mixed Integer NonLinear Programs featuring “On/Off” constraints: convex analysis and applications

2010 ◽  
Vol 36 ◽  
pp. 1153-1160 ◽  
Author(s):  
Hassan Hijazi ◽  
Pierre Bonami ◽  
Gérard Cornuéjols ◽  
Adam Ouorou
Keyword(s):  
Convex Analysis ◽  
Mixed Integer ◽  
Nonlinear Programs

Conflict Analysis for MINLP

2021 ◽  
Author(s):  
Timo Berthold ◽  
Jakob Witzig
Keyword(s):  
Nonlinear Optimization ◽  
Branch And Bound ◽  
Computational Study ◽  
General Purpose ◽  
Conflict Analysis ◽  
Mixed Integer ◽  
Mixed Integer Program ◽  
Global Optimality ◽  
Nonlinear Programs ◽  
The Impact

The generalization of mixed integer program (MIP) techniques to deal with nonlinear, potentially nonconvex, constraints has been a fruitful direction of research for computational mixed integer nonlinear programs (MINLPs) in the last decade. In this paper, we follow that path in order to extend another essential subroutine of modern MIP solvers toward the case of nonlinear optimization: the analysis of infeasible subproblems for learning additional valid constraints. To this end, we derive two different strategies, geared toward two different solution approaches. These are using local dual proofs of infeasibility for LP-based branch-and-bound and the creation of nonlinear dual proofs for NLP-based branch-and-bound, respectively. We discuss implementation details of both approaches and present an extensive computational study, showing that both techniques can significantly enhance performance when solving MINLPs to global optimality. Summary of Contribution: This original article concerns the advancement of exact general-purpose algorithms for solving one of the largest and most prominent problem classes in optimization, mixed integer nonlinear programs (MINLPs). It demonstrates how methods for conflict analysis that learn from infeasible subproblems can be transferred to nonlinear optimization. Further, it develops theory for how nonlinear dual infeasibility proofs can be derived from a nonlinear relaxation. This paper features a thoroughly computational study regarding the impact of conflict analysis techniques on the overall performance of a state-of-the-art MINLP solver when solving MINLPs to global optimality.

Lift-and-project cuts for convex mixed integer nonlinear programs

2017 ◽  
Vol 9 (4) ◽  
pp. 499-526 ◽  
Author(s):  
Mustafa R. Kılınç ◽  
Jeff Linderoth ◽  
James Luedtke
Keyword(s):  
Mixed Integer ◽  
Nonlinear Programs
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