# Branch and bound, integer, and non-integer programming

@article{Forrest2007BranchAB, title={Branch and bound, integer, and non-integer programming}, author={John J. H. Forrest and John A. Tomlin}, journal={Annals of Operations Research}, year={2007}, volume={149}, pages={81-87} }

In this note we review the development of the first commercial branch and bound codes at CEIR/Scicon, with particular emphasis on those features not commonly emphasized today that is the use of branch and bound to handle discrete constructs, which, while often formally representable in terms of zero-one integer variables, can be handled more elegantly and effectively by applying branch and bound to the actual dichotomies in the model.

## 19 Citations

MILP Software

- Computer Science
- 2010

A brief overview of state-of-the-art software for the solution of Mixed Integer Linear Programs (MILP) is given.

MINLP Solver Software

- Economics
- 2011

An overview of the start-of-the-art in software for the solution of mixed integer nonlinear programs (MINLP) is given and several groupings with respect to various features are established.

SCIP: global optimization of mixed-integer nonlinear programs in a branch-and-cut framework

- Computer ScienceOptim. Methods Softw.
- 2018

These extensions that were added to the constraint integer programming framework SCIP to enable it to solve convex and nonconvex mixed-integer nonlinear programs (MINLPs) to global optimality are described and insights into the performance impact of individual MINLP solver components are provided.

Relations between Semidefinite, Copositive, Semi-infinite and Integer Programming

- Computer Science
- 2010

This thesis will investigate the relationship to answer the question whether one can solve semidefinite program by formulating it as an equivalent eigenvalue optimization with the aid of semi-infinite programming.

The Lagrangian relaxation for the combinatorial integral approximation problem

- Mathematics, Computer ScienceOptim. Methods Softw.
- 2015

This study links the huge computational gains compared to state-of-the-art MILP solvers to an analysis of subproblems on the branching tree and proves polynomial runtime of the algorithm for special cases and numerical evidence for efficiency by means of a numerical benchmark problem.

Methods And Solvers Used For Solving Mixed Integer Linear Programming And Mixed Nonlinear Programming Problems: A Review

- Mathematics
- 2020

This paper presents a complete review of the significance of deterministic mixed -integer linear program (MILP) and mixed-integer nonlinear program (MINLP) solution methods for problems involving…

Bid Optimization for Internet Graphical Ad Auction Systems via Special Ordered Sets

- Computer ScienceArXiv
- 2007

This model is non-convex, but it is able to obtain optimal or near-optimal solutions rapidly using branch and cut open- source software.

A Jack of all Trades? Solving stochastic mixed-integer nonlinear constraint programs

- Engineering
- 2014

Natural gas is one of the most important energy sources in Germany and Europe. In recent years, political regulations have led to a strict separation of gas trading and gas transport, thereby…

Evelyn Martin Lansdowne Beale

- Computer Science
- 2011

His pioneering work on developing algorithms for real-world problems, and overseeing their implementation in large-scale commercial software systems, made a major impact on the practice of OR at the time and left a lasting imprint.

Production Planning for a Winery With Mixed Integer Programming Model

- Business
- 2009

The results obtained from a MIP model indicate that the selection of new products can favorably produce optimal schedules in the food industry and in particular to wine production.

## References

SHOWING 1-10 OF 36 REFERENCES

Practical Solution of Large Mixed Integer Programming Problems with Umpire

- Computer Science
- 1974

In this paper we discuss some branch and bound methods implemented in the UMPIRE mathematical programming system for solving practical integer programming problems and give details of computational…

An Algorithm for the Solution of Mixed Integer Programming Problems

- Business, Mathematics
- 1966

An algorithm is presented for the solution of mixed integer programming problems. The method was developed to solve primarily those programming problems which contain a large number of continuous…

ON THE SOLUTION OF DISCRETE PROGRAMMING PROBLEMS

- Economics
- 1957

Abstract : This paper considers optimization problems in which some or all variables must take on integral values. An ability to solve such problems would be valuable in itself and would also allow…

The efficient solution of large-scale linear programming problems—some algorithmic techniques and computational results

- Computer ScienceMath. Program.
- 1977

An attempt to provide a powerful mathematical programming language, allowing an easy programming of specific studies on medium-size models such as the recursive use of LP or the build-up of algorithms based on the simplex method is described.

A Suggested Extension of Special Ordered Sets to Non-Separable Non-Convex Programming Problems*

- Mathematics
- 1981

Global optimization using special ordered sets

- MathematicsMath. Program.
- 1976

Two methods for finding a global minimum of a function of a scalar variable in a finite interval, assuming that one can calculate function values and first derivatives, and also bounds on the second derivatives within any subinterval are described.

Special ordered sets and an application to gas supply operations planning

- EconomicsMath. Program.
- 1988

An application in which type 2 sets are used in several forms to model both logical conditions and nonlinear functions is described.

Linear programming and extensions

- Mathematics
- 1963

This classic book looks at a wealth of examples and develops linear programming methods for their solutions and begins by introducing the basic theory of linear inequalities and describes the powerful simplex method used to solve them.

Early Integer Programming

- EducationOper. Res.
- 2002

During the academic year 1953–54, I was a third-year graduate student in mathematics at Princeton, doing research on nonlinear differential equations, the first of which became my Ph.D. thesis.