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"... . We show that the complexity to solve linear programming problems, using standard linear algebra, can be reduced to O([n 3 = ln n]L) operations, where n is the number of variables in a standard form problem with integer data of bit size L. Our technique combines partial updating with a preconditi ..."

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. We show that the complexity to solve linear programming problems, using standard linear algebra, can be reduced to O([n 3 = ln n]L) operations, where n is the number of variables in a standard form problem with integer data of bit size L. Our technique combines partial updating with a preconditionedconjugate gradient method, in a scheme first suggestedby Nesterov and Nemirovskii. Key words. linear programming, interior point algorithm, partial updating, conjugate-gradient method AMS subject classification. 90C25 1. Introduction. Consider a standard form linear program, and its dual: LP : min c T x LD : max b T y s:t: Ax = b s:t: A T y + s = c x 0 s 0; where A is an m \Theta n matrix. We assume without loss of generality that the rows of A are linearly independent. For the purpose of stating complexity results we may assume that the data of LP is integral, and let L denote the bit size of the problem. Karmarkar's [5] celebrated projective algorithm solves LP in O(n 4 L)...