February 18 – 23 , 2018, Dagstuhl Seminar 18081

Designing and Implementing Algorithms for Mixed-Integer Nonlinear Optimization


Pierre Bonami (IBM Spain – Madrid, ES)
Ambros M. Gleixner (Konrad-Zuse-Zentrum – Berlin, DE)
Jeff Linderoth (University of Wisconsin – Madison, US)
Ruth Misener (Imperial College London, GB)

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Dagstuhl Report, Volume 8, Issue 2 Dagstuhl Report
Aims & Scope
List of Participants
Dagstuhl's Impact: Documents available
Dagstuhl Seminar Schedule [pdf]


This workshop aimed to address this mismatch between natural optimization models for important scientific problems and practical optimization solvers for their solution. By bringing together experts in both theory and implementation, this workshop energized efforts making MINLP as ubiquitous a paradigm for both modeling and solving important decision problems as mixed-integer linear programming (MIP) and nonlinear programming (NLP) have become in recent years. In particular, we highlighted:

  • MINLP Solver Software Early in the workshop, the main developers of MINLP software packages outlined the current state of their software. This served as a needs analysis for the community to identify crucial areas for future development. We also dedicated a break-out session discussing best practices for conducting scientifically-meaningful computational experiments in MINLP.
  • Intersecting Mixed-Integer & Nonlinear Programming MINLP is a superset of both mixed integer linear optimization and nonlinear optimization, so we leveraged the best methods from both by incorporating both sets of experts.
  • Driving Applications Applications experts, e.g. in petrochemicals, manufacturing, and gas networks, offered their perspectives on what practitioners need from MINLP solvers. We dedicated an entire break-out session to energy applications and explored what are the needs for MINLP within the energy domain. During the open problem session, several other applications experts outlined other open problems in engineering.
  • Connections between MINLP and machine learning Many machine learning challenges can be formulated as MINLP. Also, machine learning can significantly improve MINLP solver software. We explored these connections at length in a break-out session.

This seminar brought together an assortment of computer scientists with expertise in mathematical optimization. Many of the presentations were more theoretical and suggested new technologies that the solver software could incorporate. Other presentations were more practical and discussed building solver software or applying that software to specific domain applications.

As a result of this seminar, we are planning a special issue in the journal "Optimization & Engineering". We are also working to turn the notes from our open problem session into a larger document that will start a conversation with the entire mathematical optimisation community. Participants broadly expressed that this week at Dagstuhl helped them workshop their papers, so several academic papers will explicitly mention the Dagstuhl seminar. Finally, a new set of metrics for comparing MINLP solvers were developed at this meeting and will greatly aid future solver testing.

Summary text license
  Creative Commons BY 3.0 Unported license
  Pierre Bonami, Ambros M. Gleixner, Jeff Linderoth, and Ruth Misener


  • Data Structures / Algorithms / Complexity
  • Optimization / Scheduling


In the series Dagstuhl Reports each Dagstuhl Seminar and Dagstuhl Perspectives Workshop is documented. The seminar organizers, in cooperation with the collector, prepare a report that includes contributions from the participants' talks together with a summary of the seminar.


Download overview leaflet (PDF).

Dagstuhl's Impact

Please inform us when a publication was published as a result from your seminar. These publications are listed in the category Dagstuhl's Impact and are presented on a special shelf on the ground floor of the library.


Furthermore, a comprehensive peer-reviewed collection of research papers can be published in the series Dagstuhl Follow-Ups.