# An algorithm for mixed integer optimization

@article{Kppe2003AnAF, title={An algorithm for mixed integer optimization}, author={Matthias K{\"o}ppe and Robert Weismantel}, journal={Mathematical Programming}, year={2003}, volume={98}, pages={281-307} }

Abstract.This paper introduces a new algorithm for solving mixed integer programs. The core of the method is an iterative technique for changing the representation of the original mixed integer optimization problem.

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## References

SHOWING 1-10 OF 18 REFERENCES

### AN ALGORITHM FOR THE MIXED INTEGER PROBLEM

- Mathematics
- 1960

Abstract : An algorithm is given for the numerical solution of the 'mixed integer' linear programming problem, the problem of maximizing a linear form in finitely many variables constrained both by…

### The integral basis method for integer programming

- Computer ScienceMath. Methods Oper. Res.
- 2001

An exact algorithm for solving integer programs, neither using cutting planes nor enumeration techniques, that relies on iteratively substituting one column by columns that correspond to irreducible solutions of certain linear diophantine inequalities.

### A primal all-integer algorithm based on irreducible solutions

- Mathematics, Computer ScienceMath. Program.
- 2003

An exact primal augmentation algorithm for solving general linear integer programs that iteratively substitutes one column in a tableau by other columns that correspond to irreducible solutions of certain linear diophantine inequalities is introduced.

### Integral decomposition of polyhedra and some applications in mixed integer programming

- MathematicsMath. Program.
- 2003

It is shown that there is a finite subset of this family of rational polyhedra that generates the entire family and an integer analogue of Carathéodory's theorem carries over to this general setting.

### A Simplified Primal (All-Integer) Integer Programming Algorithm

- Computer ScienceOper. Res.
- 1968

The simplified primal algorithm makes these major amendments to the simplex method: a special row, indexed by L, is adjoined to the tableau and is periodically revised by a well-defined procedure.

### Solving a System of Linear Diophantine Equations with Lower and Upper Bounds on the Variables

- Mathematics, Computer ScienceMath. Oper. Res.
- 2000

An algorithm for solving constrained diophantine equations as subproblems when designing integrated circuits for video signal processing based on lattice basis reduction, which is tested with good results on real-life data, and on instances from the literature.

### Solving a System of Diophantine Equations with Lower and Upper Bounds on the Variables

- Mathematics
- 1998

We develop an algorithm for solving a system of diophantine equations with lower and upper bounds on the variables. The algorithm is based on lattice basis reduction. It rst nds a short vector…

### A lift-and-project cutting plane algorithm for mixed 0–1 programs

- Computer ScienceMath. Program.
- 1993

We propose a cutting plane algorithm for mixed 0–1 programs based on a family of polyhedra which strengthen the usual LP relaxation. We show how to generate a facet of a polyhedron in this family…

### The IntegralBasisMethod for integer programming

- Mathematical Methods of Operations Research,
- 2001