Learning from Both Sides Linear and Nonlinear Mixed-Integer Optimization

Optimization problems are categorized based on the types of variables and functions in their mathematical description, where mixed-integer linear programming (MILP) and mixed-integer nonlinear programming (MINLP) are two of the most general classes. Both classes of problems have been actively studied in the last decades due to their challenging mathematical properties and their remarkable versatility in representing complex processes and phenomena. MINLP problems are of great interest in applied mathematics as they combine numerical challenges of solving large nonlinear systems with combinatorial challenges, resulting in problems that are truly complex to solve. Research in the field is also driven by a large range of important applications across science and engineering.

Different research communities have formed around MILP and MINLP, even if the two are closely related. Historically, MILP and MINLP have been developed from different perspectives. MILP has been studied more in-depth from a mathematical perspective, and the theoretical foundation is stronger for linear problems. MILP is closely related to the fields of combinatorics and discrete geometry, and it can be viewed as a generalization of combinatorial optimization. Research in MINLP instead, has been more application driven. Several of the main contributions, both theoretical and algorithmic, originate from engineering. However, MINLP is also of great interest from a pure mathematical perspective and it is an active area for fundamental research.

The goal of the workshop is to bring together leading researchers from both the MILP and MINLP communities to discuss current challenges in the respective fields and transfer knowledge between the two. We believe that great mutual benefits can be obtained by learning from “the other side”. As the two communities have focused on somewhat different aspects, we believe that both communities can learn from each other when it comes to techniques, theory, and methods for dealing with challenging mixed-integer problems.