# Oliver Stein: The Granularity Concept in Mixed-Integer Optimization

Abstract

Granularity of optimization problems relaxes the difficulties imposed by integrality conditions and often

provides ways for determining good feasible points of mixed-integer optimization problems at low computational cost.

It thus provides so-called primal heuristics while, in fact, it is not based on heuristic ideas, but on transparent

geometric considerations.

Starting from error bound results for roundings in mixed-integer linear optimization, we illustrate

how the granularity concept unfolds to provide algorithms for the computation of feasible points in mixed-integer

linear, convex and nonconvex optimization. We also comment on the treatment of equality constraints and

explain the integration of the granularity idea into branch-and-bound frameworks.

**Time: **
Thu 2022-06-09 11.00 - 12.00

**Location: **
Seminar room 3721

**Video link: **
Zoom ID 63658381373

**Language: **
English

**Participating: **
Oliver Stein, Karlsruhe Institute of Technology (KIT), stein@kit.edu