Linear Programming Part II: Interior-Point Methods
A paper by Karmarkar in 1984  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  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 .
KeywordsLinear Program Problem Central Path Apply Algorithm Barrier Parameter Logarithmic Barrier Function
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