Outer approximation algorithms for separable nonconvex mixed-integer nonlinear programs

2004 ◽  
Vol 100 (3) ◽  
Author(s):  
Padmanaban Kesavan ◽  
Russell J. Allgor ◽  
Edward P. Gatzke ◽  
Paul I. Barton
Keyword(s):  
Approximation Algorithms ◽  
Outer Approximation ◽  
Mixed Integer ◽  
Nonlinear Programs

Solving mixed integer nonlinear programs by outer approximation

1994 ◽  
Vol 66 (1-3) ◽  
pp. 327-349 ◽  
Author(s):  
Roger Fletcher ◽  
Sven Leyffer
Keyword(s):  
Outer Approximation ◽  
Mixed Integer ◽  
Nonlinear Programs

FilMINT: An Outer Approximation-Based Solver for Convex Mixed-Integer Nonlinear Programs

2010 ◽  
Vol 22 (4) ◽  
pp. 555-567 ◽  
Author(s):  
Kumar Abhishek ◽  
Sven Leyffer ◽  
Jeff Linderoth
Keyword(s):  
Outer Approximation ◽  
Mixed Integer ◽  
Nonlinear Programs

scholarly journals Partially distributed outer approximation

2021 ◽  
Author(s):  
Alexander Murray ◽  
Timm Faulwasser ◽  
Veit Hagenmeyer ◽  
Mario E. Villanueva ◽  
Boris Houska
Keyword(s):  
Large Scale ◽  
Optimization Problems ◽  
Outer Approximation ◽  
Mixed Integer ◽  
Global Optimality ◽  
Integer Optimization ◽  
Global Minimizers ◽  
Outer Approximation Method ◽  
Coupling Constraints ◽  
Outer Approximation Algorithm

AbstractThis paper presents a novel partially distributed outer approximation algorithm, named PaDOA, for solving a class of structured mixed integer convex programming problems to global optimality. The proposed scheme uses an iterative outer approximation method for coupled mixed integer optimization problems with separable convex objective functions, affine coupling constraints, and compact domain. PaDOA proceeds by alternating between solving large-scale structured mixed-integer linear programming problems and partially decoupled mixed-integer nonlinear programming subproblems that comprise much fewer integer variables. We establish conditions under which PaDOA converges to global minimizers after a finite number of iterations and verify these properties with an application to thermostatically controlled loads and to mixed-integer regression.

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.

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