Mixed-Integer Nonlinear Optimization: Algorithmic Advances and Applications

Many engineering, operations, and scientific applications involve both discrete decisions and nonlinear relationships that significantly affect the feasibility and optimality of solutions. Mixed-integer nonlinear programming (MINLP) problems combine the difficulty of optimizing over discrete variable sets with the challenges of handling nonlinear functions. MINLP is one of the most flexible modeling paradigms available: An expanding body of researchers and practitioners, including chemical engineers, operations researchers, industrial engineers, mechanical engineers, economists, statisticians, computer scientists, operations managers, and mathematical programmers are interested in solving large-scale MINLPs.

Unfortunately, the wealth of applications that can be accurately modeled by using MINLP is not yet matched by the capability of available optimization solvers. Yet, the two components of MINLP, namely mixed-integer linear programming (MIP), and nonlinear programming (NLP), have witnessed tremendous progress over the past 15 years. By cleverly incorporating many theoretical advances in MIP research, powerful academic, open source, and commercial solvers paved the way for MIP to emerge as a viable, widely used decision-making tool. Similarly, new paradigms and a better theoretical understanding have created faster and more reliable NLP solvers that work well even under adverse conditions such as failures of constraint qualifications.

The time is right to synthesize these advances and inspire new ideas in order to transform MINLP into an area in which researchers and practitioners can access robust tools and methods capable of solving a wide range of important, commonly occurring decision support problems. This workshop brings together experts from relevant optimization areas to exchange recent results on MINLP, chart the future of MINLP, explore new and innovative applications, and outline the challenges facing this area. The workshop will discuss novel solution approaches and the impact of new powerful computational resources to solve MINLP problems.