# 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.

## 12 Citations

### A Generalized Upper Bounding Method for Doubly Coupled Linear Programs

- Mathematics, Computer Science
- 1970

Abstract : The algorithm proposed is an extension of the generalized upper bounding method for problems without coupling columns. It produces the same sequence of extreme point solutions as the…

### Elements of Large Scale Mathematical Programming Part II: Synthesis of Algorithms and Bibliography

- Computer Science
- 1970

The problem manipulations and solution strategies of Part I of this paper are now further illustrated by combining them in various ways to yield several known algorithms. The main object is not an…

### A primal algorithm for solving a capacitated network flow problem with additional linear constraints

- Computer ScienceNetworks
- 1977

A variant of the revised simplex method is given for solving capacitated network flow problems with additional linear constraints for pivoting, pricing, and inversion that can result in a substantial reduction of computation over a standard linear programming approach.

### Computational improvements to Benders decomposition for generalized fixed charge problems

- Computer Science
- 1973

A computationally efficient algorithm has been developed for determining exact or approximate solutions for large scale generalized fixed charge problems, based on a relaxation of the Benders decomposition procedure and a computationally improved generalized upper bounding (GUB) algorithm which solves a convex separable programming problem by generalized linear programming.

### Scalable Massively Parallel Simplex Algorithms for Block-structured Lp Problems

- Computer Science
- 1997

The design and implementation of a massively parallel simplex algorithm for Generalized Upper Bounded (GUB) LP Problems are described from the point of view of scalability and portability and the numerical stability of the data-parallel Dense Tableau Simplex (DTS) code is particularly surprising.

### Basis Factorization for Block-Angular Linear Problems: Unified Theory of Partitioning and Decomposition using the Simplex Method

- Computer Science
- 1974

A General Block-Angular Basis Factorization is developed to represent the inverse of the basis of block-angular linear problems in factorized form. This factorization takes advantage of the structure…

### A column generation and partitioning approach for multi-commodity flow problems

- Computer Science, EconomicsTelecommun. Syst.
- 1994

This paper presents a partitioning solution procedure for large-scale multi-commodity flow problems with many commodities, such as those encountered in the telecommunications industry, using a cycle-based multi- commodity formulation and column generation techniques.

### The Solution of Multiperiod Network Models with Bundle Constraints by Aggregation

- Computer Science
- 1993

A new network aggregation/disaggregation approach for solving a multiperiod, network model with bundle Generalized Upper Bounding side constraints with very tight "computational" error bound is presented.

## References

SHOWING 1-4 OF 4 REFERENCES

### An Approach to Some Structured Linear Programming Problems

- Business, MathematicsOper. Res.
- 1966

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

- Mathematics
- 1962

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

- 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.