# Title: (Convex) Mixed-Integer Nonlinear programming

This talk will mainly focus on algorithms and solvers for convex MINLP.

Abstract

Mixed integer nonlinear programming (MINLP) offers a flexible framework for dealing with a wide variety of optimizations tasks, but it also inherits the combinatorial challenges from integer programming and numerical challenges from nonlinear programming. MINLP problems are automatically nonconvex due to the integer restrictions; however, they are still commonly classified as either convex or nonconvex based on their continuous relaxation. Convexity is a desirable property since it enables a straightforward decomposition of the problem into a sequence of tractable subproblems.

During the last decades, several algorithms have been presented for convex MINLP, such as nonlinear branch and bound, generalized Bender’s decomposition, and several algorithms based on polyhedral outer approximations. The most common algorithms will be presented during the talk, and we examine some convergence properties of the algorithms. Some important solver features will also be discussed, and we look at the convex MINLP solver SHOT in more detail.

**Time: **
Fri 2019-05-17 11.00 - 12.00

**Lecturer: **
Jan Kronqvist,

**Location: ** F11

Jan Kronqvist Royal Society - Newton International Research Fellow Department of Computing, Imperial College London