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A simplified homogeneous and selfdual linear programming algorithm and its implementation
 Annals of Operations Research
, 1996
"... 1 Introduction Consider the linear programming (LP) problem in the standard form: (LP) minimize cT x ..."
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Cited by 56 (5 self)
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1 Introduction Consider the linear programming (LP) problem in the standard form: (LP) minimize cT x
An Asymptotical O(...)iteration Pathfollowing Linear Programming Algorithm That Uses Wide Neighborhoods
, 1994
"... Pathfollowing linear programming (LP) algorithms generate a sequence of points within certain neighborhoods of a centralpath C, which prevent iterates from prematurely getting too close to the boundary of the feasible region. Depending on their norm used, these neighborhoods include N2(fi), N1(fi) ..."
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Pathfollowing linear programming (LP) algorithms generate a sequence of points within certain neighborhoods of a centralpath C, which prevent iterates from prematurely getting too close to the boundary of the feasible region. Depending on their norm used, these neighborhoods include N2(fi), N1(fi) and N \Gamma 1(fi), where fi 2 (0; 1), and C ae N2(fi) ae N1(fi) ae N \Gamma 1(fi) for each fi 2 (0; 1): A paradox is that among all existing (infeasible or feasible) pathfollowing algorithms, the theoretical iteration complexity, O(pnL), of smallneighborhood (N2) algorithms is significantly better than the complexity, O(nL), of wideneighborhood (N \Gamma 1) algorithms, while in practice wideneighborhood algorithms outperform smallneighborhood ones by a big margin. Here, n is the number of LP variables and L is the LP data length. In this paper, we present an O(n n+1 2n L)iteration (infeasible) primaldual highorder algorithm that uses wide neighborhoods. Note that this iteration bound is asymptotical O(pnL), i.e., the best bound for smallneighborhood algorithms, as n increases.