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Designing and Implementing Algorithms for Mixed-Integer Nonlinear Optimization (Dagstuhl Seminar 18081)

Pierre Bonami, Ambros M. Gleixner, Jeff Linderoth, Ruth Misener, Michael Wagner
2018 Dagstuhl Reports  
These mixed-integer nonlinear programs (MINLP) may be used to optimize the energy use of large industrial plants, integrate renewable sources into energy networks, design biological and biomedical systems  ...  Mathematical models for optimal decisions often require both nonlinear and discrete components.  ...  for Mixed-Integer Nonlinear Optimization -Algorithms for Mixed-Integer Nonlinear Optimization  ... 
doi:10.4230/dagrep.8.2.64 dblp:journals/dagstuhl-reports/BonamiGLM18 fatcat:fn6llvricbevzjsm4teuf5xuha

Mixed-integer nonlinear programming 2018

Nikolaos V. Sahinidis
2019 Optimization and Engineering  
Mixed-Integer Nonlinear Programming (MINLP) is the area of optimization that addresses nonlinear problems with continuous and integer variables. MINLP has proven to be a powerful tool for modeling.  ...  At the same time, it combines algorithmic design challenges from combinatorial and nonlinear optimization.  ...  (2019) present a modification to the classical successive linear programming algorithm for solving nonlinear and mixed-integer nonlinear optimization problems.  ... 
doi:10.1007/s11081-019-09438-1 fatcat:yicrfo52abhdjcf3sf2xbd24s4

A Branch-and-Cut Algorithm for Mixed-Integer Bilinear Programming

Matteo Fischetti, Michele Monaci
2019 European Journal of Operational Research  
For this problem we describe a branch-and-cut algorithm for its exact solution, based on a new family of intersection cuts derived from bilinear-specific disjunctions.  ...  Our results show that our method, even without intersection cuts, is competitive with a state-of-the-art mixed-integer nonlinear solver.  ...  We thank the organizers of Dagstuhl Seminar 18081 "Designing and Implementing Algorithms for Mixed-Integer Nonlinear Optimization" (Pierre Bonami, Ambros M.  ... 
doi:10.1016/j.ejor.2019.09.043 fatcat:dbpm42yrtrg5pdysgz4g6yzkp4

A review and comparison of solvers for convex MINLP

Jan Kronqvist, David E. Bernal, Andreas Lundell, Ignacio E. Grossmann
2018 Optimization and Engineering  
To show how the solvers perform on problems with different properties, we have divided the test set into subsets based on the continuous relaxation gap, the degree of nonlinearity, and the relative number  ...  The results also provide guidelines on how well suited a specific solver or method is for particular types of MINLP problems.  ...  The authors want to acknowledge the Dagstuhl Seminar 18081 on Designing and Implementing Algorithms for Mixed-Integer Nonlinear Optimization, which provided valuable insight into the current status of  ... 
doi:10.1007/s11081-018-9411-8 fatcat:qwbcge5wkrdmrp6qww7x3llncu

On Generalized Surrogate Duality in Mixed-Integer Nonlinear Programming [article]

Benjamin Müller, Gonzalo Muñoz, Maxime Gasse, Ambros Gleixner, Andrea Lodi, Felipe Serrano
2019 arXiv   pre-print
The most important ingredient for solving mixed-integer nonlinear programs (MINLPs) to global epsilon-optimality with spatial branch and bound is a tight, computationally tractable relaxation.  ...  These relaxations were actively studied for linear integer programs in the 70s and 80s, but they have been scarcely considered since.  ...  The authors thank the Schloss Dagstuhl -Leibniz Center for Informatics for hosting the Seminar 18081 "Designing and Implementing Algorithms for Mixed-Integer Nonlinear Optimization" for providing the environment  ... 
arXiv:1912.00356v1 fatcat:f3hmuz6vajb23pp2apnd4sdc4a

On Generalized Surrogate Duality in Mixed-Integer Nonlinear Programming [chapter]

Benjamin Müller, Gonzalo Muñoz, Maxime Gasse, Ambros Gleixner, Andrea Lodi, Felipe Serrano
2020 Lecture Notes in Computer Science  
The most important ingredient for solving mixed-integer nonlinear programs (MINLPs) to global -optimality with spatial branch and bound is a tight, computationally tractable relaxation.  ...  These relaxations were actively studied for linear integer programs in the 70s and 80s, but they have been scarcely considered since.  ...  The authors thank the Schloss Dagstuhl -Leibniz Center for Informatics for hosting the Seminar 18081 "Designing and Implementing Algorithms for Mixed-Integer Nonlinear Optimization" for providing the environment  ... 
doi:10.1007/978-3-030-45771-6_25 fatcat:hrxrj7tnb5bo3e2xiai5jx4tfm

A Method for Convex Black-Box Integer Global Optimization [article]

Jeffrey Larson, Sven Leyffer, Prashant Palkar, Stefan M. Wild
2020 arXiv   pre-print
We also compare implementations of our algorithm with existing methods for minimizing functions on a subset of the integer lattice.  ...  We discuss the difficulty of this problem class and provide insights into why a computational proof of optimality is challenging even for moderate problem sizes.  ...  Acknowledgements We are grateful to Eric Ni for his insights on derivative-free algorithms for unrelaxable integer variables.  ... 
arXiv:1903.11366v2 fatcat:jtkbdvi7yza3rg53zminpjuwtm

Upcoming Press-Relevant Seminars and Perspectives Workshops

Jeremy Blackburn, Michael Sirivianos, Thorsten Strufe, T Dresden
unpublished
This list provides the following information for press relevant Dagstuhl Seminars: names and affiliations of all members of the organizing team including the coordinators; arrival and departure dates;  ...  and protected.This Dagstuhl Seminar will bring together researchers working on all aspects of cybersafety, including security, privacy, human factors, economics, sociology.  ...  designs, and on (secure) routing for highly-mobile scenarios including ad-hoc networks, sensor networks, robotic (swarm) networks, delay-tolerant networks and vehicular networks.  ... 
fatcat:rkfp7mvcajbkxntv4cgx27rtsm

Using Two-Dimensional Projections for Stronger Separation and Propagation of Bilinear Terms

Benjamin Müller, Felipe Serrano, Ambros Gleixner
2020 SIAM Journal on Optimization  
One of the most fundamental ingredients in mixed-integer nonlinear programming solvers is the well-known McCormick relaxation for a product of two variables x and y over a boxconstrained domain.  ...  In order to exploit this in practice, we propose to compute valid linear inequalities for the projection of the feasible region onto the x-y-space by solving a sequence of linear programs akin to optimization-based  ...  The authors thank the Schloss Dagstuhl -Leibniz Center for Informatics for hosting the Seminar 18081 "Designing and Implementing Algorithms for Mixed-Integer Nonlinear Optimization" for providing the environment  ... 
doi:10.1137/19m1249825 fatcat:u32oo65hxbgpxpqhf2sdyxfi7i

Using two-dimensional Projections for Stronger Separation and Propagation of Bilinear Terms [article]

Benjamin Müller, Felipe Serrano, Ambros Gleixner
2020 arXiv   pre-print
One of the most fundamental ingredients in mixed-integer nonlinear programming solvers is the well-known McCormick relaxation for a product of two variables x and y over a box-constrained domain.  ...  As a consequence, we obtain a stronger convexification procedure that exploits problem structure and can benefit from supplementary information obtained during the branch-and-bound algorithm such as an  ...  The authors thank the Schloss Dagstuhl -Leibniz Center for Informatics for hosting the Seminar 18081 "Designing and Implementing Algorithms for Mixed-Integer Nonlinear Optimization" for providing the environment  ... 
arXiv:1903.05521v2 fatcat:sy5xzfjc6rachiwd55ljvob5vy