SHORT COURSEI. Title:A Practical Guide to Mixed Integer Nonlinear Programming II. ShortCourse Organizers:Sven Leyffer, Argonne National Laboratory, III. Associated SIAM Conference:Eighth SIAM Conference on Optimization IV. Rationale: Many optimization problems involve both nonlinear constraints to model V. Instructors:Sven Leyffer is a scientist at Argonne National Laboratory. He has worked on integer nonlinear optimization, nonlinear optimization, and optimization problems with equilibrium constraints. Jeff Linderoth is an assistant professor at Lehigh University. His interests include mixed integer linear optimization, and stochastic programming. VI. Course Description:The course will start by considering examples of MINLPs, showing how they arise in a variety of application areas. Through the applications, the students will be introduced to a variety of modeling techniques for MINLP. The second part reviews classical methods for MINLP, such as nonlinear branchandbound (BB), and decomposition schemes, such as outer approximation and Benders decomposition. We show how these methods can be improved by using inexact solves and hybrid approaches. The third part of the course provides an introduction to more recent developments in MINLP, including the extension of cutting planes from MILP to MINLP, direct disjunctive formulations, and underestimation methods for nonconvex problems. The final part of the course discusses software for MINLP and implementation details of the various available packages, including comparative computational results. We also present a parallel BB approach that solves large MINLP on a computational grid. VII. Level of the Material:The target audience is both graduate students and researchers working in nonlinear programming and mixed integer optimization. The course does not require any knowledge beyond an undergraduate course in nonlinear optimization and some familiarity with AMPL. Course Outline Introduction, Applications, and Formulations: (1 hour)
Methods for Convex MINLP: (2 hours)
Advanced Methods for MINLP: (2 hours)
Implementation and Software: (1.5 hours)


