论文信息 - A Jordan-algebraic approach to potential-reduction algorithms

A Jordan-algebraic approach to potential-reduction algorithms

Abstract. We consider the linear monotone complementarity problem for domains obtained as the intersection of an affine subspace and the Cartesian product of symmetric cones. A primal-dual potential reduction algorithm is described and its complexity estimates are established with the help of the Jordan-algebraic technique.

L. Faybusovich

[1] M. Koecher. Jordan algebras and their applications , 1962 .

[2] Shinji Mizuno,et al. An $$O(\sqrt n L)$$ iteration potential reduction algorithm for linear complementarity problems , 1991, Math. Program..

[3] J. Faraut,et al. Analysis on Symmetric Cones , 1995 .

[4] Harald Upmeier,et al. Toeplitz Operators and Index Theory in Several Complex Variables , 1995 .

[5] Michael J. Todd,et al. Potential-reduction methods in mathematical programming , 1997, Math. Program..

[6] Pseudodifferential Analysis on Symmetric Cones , 1996 .

[7] Michael J. Todd,et al. Self-Scaled Barriers and Interior-Point Methods for Convex Programming , 1997, Math. Oper. Res..

[8] L. Faybusovich. Linear systems in Jordan algebras and primal-dual interior-point algorithms , 1997 .

[9] Stephen J. Wright. Primal-Dual Interior-Point Methods , 1997, Other Titles in Applied Mathematics.

[10] L. Faybusovich. Euclidean Jordan Algebras and Interior-point Algorithms , 1997 .