Practical Optimization pp 373-406 | Cite as

# Linear Programming Part II: Interior-Point Methods

## Abstract

A paper by Karmarkar in 1984 [1] and substantial progress made since that time have led to the field of modern *interior-point methods* for linear programming (LP). Unlike the family of simplex methods considered in Chap. 11, which approach the solution through a sequence of iterates that move from vertex to vertex along the edges on the boundary of the feasible polyhedron, the iterates generated by interior-point algorithms approach the solution from the *interior* of a polyhedron. Although the claims about the efficiency of the algorithm in [1] have not been substantiated in general, extensive computational testing has shown that a number of interior-point algorithms are much more efficient than simplex methods for large-scale LP problems [2].

## Keywords

Linear Program Problem Central Path Apply Algorithm Barrier Parameter Logarithmic Barrier Function## Preview

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## References

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