I. J. Lustig, "A generic primal-dual interior point algorithm," Technical Report SOR 88-3, Program in Statistics and Operations Research, Department of Civil Engineering and Operations Research, Princeton University (Princeton, New Jersey, 1988).  Home/Search   Document Not in Database   Summary   Related Articles

....at least linearly with a ratio of (1 Gamma ffi= p n) in every iteration. Hence, the convergence of the duality gap to zero is too slow in practice when n is large. In view of the above, a smaller search direction parameter fi seems necessary to increase the efficiency of the GPD method. Lustig [14] discussed a region in the space of the search direction and step length parameters in which the GPD method converges globally. Mizuno, Todd and Ye [21] proposed an O(nL) iteration PD algorithm where they took fi = fi 0 in every iteration with an arbitrary fixed fi 0 2 (0; 1) and a larger ....

....from 1 to zero as (x; y; z) 2 S moves away from the central path S cen and approaches the boundary of S . Thus, 1 Gamma (x; y; z) represents a deviation from S cen . For simplicity of notation, we use k for (x k ; y k ; z k ) Remark. Kojima, Mizuno and Yoshise [11] and Lustig [14] used 1= which they denoted by , to measure a deviation from the central path S cen . See also [9] for some other quantities to measure a deviation from the central path S cen and their relation to . It follows from the Newton equation (3) which is satisfied by ( Deltax; Deltay; Deltaz) ....

I. J. Lustig, "A generic primal-dual interior point algorithm," Technical Report SOR 88-3, Program in Statistics and Operations Research, Department of Civil Engineering and Operations Research, Princeton University (Princeton, New Jersey, 1988).

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