Integer programming is a crucial branch of mathematical optimisation that focuses on problems where some or all decision variables are constrained to be integers. This field underpins many practical ...

That was almost 50 years ago; since then, Microsoft has embraced open-source software. In recent years, Microsoft has started ...

Roughly, we will cover the following topics (some of them may be skipped depending on the time available). Linear Programming: Basics, Simplex Algorithm, and Duality. Applications of Linear ...

The feasibility pump is a well-established primal heuristic for mixed integer programming (MIP) that alternates between solving a linear programming (LP) relaxation of the original problem and ...

A two-person, noncooperative game in which the players move in sequence can be modeled as a bilevel optimization problem. In this paper, we examine the case where each player tries to maximize the ...