An Extension of Generalized Upper Bounding Techniques for Structured Linear Programs

@article{Sakarovitch1967AnEO,
  title={An Extension of Generalized Upper Bounding Techniques for Structured Linear Programs},
  author={M. Sakarovitch and Romesh Saigal},
  journal={Siam Journal on Applied Mathematics},
  year={1967},
  volume={15},
  pages={906-914}
}
An algorithm is developed for solving a special structured linear program. The particular structure studied has a large number of blocks coupled together by relatively few connecting equations. The method proposed is an extension of [2] and, from the basis, defines a working basis which is much smaller in size than the original. Two methods of updating the working basis are proposed. 

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References

SHOWING 1-4 OF 4 REFERENCES

Generalized Upper Bounding Techniques

An Approach to Some Structured Linear Programming Problems

The work describes a computational approach, which is alternative to that of Dantzig and Wolfe, for handling structured linear programming problems that would break up into a number of subproblems

COMPACT BASIS TRIANGULARIZATION FOR THE SIMPLEX METHOD

Abstract : The inv rse of the basis in the simplex method serves no function except as a means for obtaining the representation of the vector entering the basis and for determining the new price

Linear programming and extensions

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.