P. Tseng. Analysis of infeasible path-following methods using the Alizadeh-Haeberly-Overton direction for the monotone semidefinite lcp. Technical report, Department of Mathematics, University of Washington, Seattle, Washington 98195, U.S.A., 1996.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....direction is a solution of (7) 8) and #XZ Z#X #ZX= XZ ZX) 13) Several convergence properties including polynomial time convergence are known for the path following algorithm using the AHO direction. See for example the work of Kojima, Shida and Shindoh [17] Monteiro [22] and Tseng [36]. The AHO direction however, is not necessarily well defined on the feasible region as observed by Shida, Shindoh and Kojima [33] the linear system (7) 8) and (13) can be inconsistent for some problems. In fact, a specific example was given by Todd, Toh and Tutuncu [35] On the other hand, ....

P. Tseng. Analysis of infeasible path-following methods using the Alizadeh-Haeberly-Overton direction for the monotone semidefinite lcp. Technical report, Department of Mathematics, University of Washington, Seattle, Washington 98195, U.S.A., 1996.

....of (7) 8) and X#Z #X Z Z#X #Z X = X Z Z X ) 13) Several convergence properties including polynomial time convergence are known for the path following algorithm using the AHO direction. See for example the work of Kojima, Shida and Shindoh [17] Monteiro [22] and Tseng [36]. The AHO direction however, is not necessarily well defined on the feasible region as observed by Shida, Shindoh and Kojima [33] the linear system (7) 8) and (13) can be inconsistent for some problems. In fact, a specific example was given by Todd, Toh and Tutuncu [35] On the other hand, ....

P. Tseng. Analysis of infeasible path-following methods using the Alizadeh-Haeberly-Overton direction for the monotone semidefinite lcp. Technical report, Department of Mathematics, University of Washington, Seattle, Washington 98195, U.S.A., 1996.

....and X DeltaZ DeltaX Z Z DeltaX DeltaZ X = Gamma(X Z ZX) 13) Several convergence properties including polynomial time convergence are known for the path following algorithm using the AHO direction. See for example the work of Kojima, Shida and Shindoh [17] Monteiro [22] and Tseng [35]. The AHO direction however, is not necessarily well defined on the feasible region as observed by Shida, Shindoh and Kojima 4 [32] the linear system (6) 7) and (13) can be inconsistent for some problems. In fact, a specific example was given by Todd, Toh and Tutuncu [34] On the other ....

P. Tseng. Analysis of infeasible path-following methods using the Alizadeh-HaeberlyOverton direction for the monotone semidefinite lcp. Technical report, Department of Mathematics, University of Washington, Seattle, Washington 98195, U.S.A., 1996.

....of (6) 7) and X#Z #X Z Z#X #Z X = X Z Z X ) 12) Several convergence properties including polynomial time convergence are known for the path following algorithm using the AHO direction. See for example the work of Kojima, Shida and Shindoh [18] Monteiro [23] and Tseng [39]. The AHO direction however, is not necessarily well defined on the feasible region as observed by Shida, Shindoh and Kojima [36] the linear system (6) 7) and (12) can be inconsistent for some problems. In fact, a specific example was given by Todd, Toh and Tutuncu [38] On the other hand, ....

P. Tseng. Analysis of infeasible path-following methods using the Alizadeh-Haeberly-Overton direction for the monotone semidefinite lcp. Technical report, Department of Mathematics, University of Washington, Seattle, Washington 98195, U.S.A., 1996.

....and to other contexts. For example, both Lemma 1 and Prop. 1 can be extended to monotone semidefinite linear complementarity problem where, instead of n , we work in the space of n Theta n symmetric real matrices and componentwise nonnegativity is replaced by nonnegativity of the eigenvalues [38]. It may be possible to extend our analysis to H based on the Kanzow smoothing function q x 2 i y 2 i 2 [16] as well as to nonsmooth Newton methods, but further study would be required. ....

Tseng, P. (1996), "Analysis of infeasible path-following methods using the Alizadeh-Haeberly-Overton direction for the monotone semi-definite LCP," Report, Department of Mathematics, University of Washington, Seattle.

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