L. Vandenberghe, S. Boyd, Positive-Definite Programming, Mathematical Programming: State of the Art 1994, J.R. Birge and K.G. Murty ed.s, U. of Michigan, 1994. Home/Search Document Not in Database Summary Related Articles Check |
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Some Geometric Results in Semidefinite Programming - Ramana, Goldman (1995) (7 citations) (Correct)
....LP into polynomial time algorithms for solving SDPs approximately. Independently of Alizadeh s work, Nesterov and Nemirovskii[NN94] developed efficient interior point methods for a wider class of convex programs, by employing self concordant barrier functions. We refer the reader to [Ali94] and [VB94] for an account of several algorithmic approaches to SDP as well as its applications. A very recent result of Goemans and Williamson[GW94] showing that one can use the solution obtained from a semidefinite relaxation to obtain a :878 approximation algorithm for the Max Cut problem, gives further ....
L. Vandenberghe, S. Boyd, Positive-Definite Programming, Mathematical Programming: State of the Art 1994, J.R. Birge and K.G. Murty ed.s, U. of Michigan, 1994.
An Exact duality Theory for Semidefinite Programming and its.. - Ramana (1995) (24 citations) Self-citation (Programming) (Correct)
....conditions are restrictive in practical applications, they severely limit the applicability of LSD for many theoretical concerns, such as Farkas type Lemmas. The following is an extremely simple SDP, for which the LSD entertains a nonzero duality gap (slight modification of an example in [VB94]) Example 1: SDP for which LSD has a duality gap Let the primal be sup : x 2 s.t. 2 4 x 2 0 0 0 x 1 x 2 0 x 2 0 3 5 2 4 ff 0 0 0 0 0 0 0 0 3 5 where ff 0. Then the LSD becomes: inf : ffU 11 s.t. U 22 = 0 U 11 2U 23 = 1 U 0 Any primal feasible solution has x 2 = 0, and hence ....
L. Vandenberghe, S. Boyd, Positive-Definite Programming, Mathematical Programming: State of the Art 1994, J.R. Birge and K.G. Murty ed.s, U. of Michigan, 1994.
An Exact duality Theory for Semidefinite Programming and its .. - Motakuri Venkata Self-citation (Programming) (Correct)
....conditions are restrictive in practical applications, they severely limit the applicability of LSD for many theoretical concerns, such as theorems of the alternative (see x1.4. 3) The following is a very simple SDP, for which the LSD had a nonzero duality gap (slight modification of an example in [VB94]) Example 1: SDP for which LSD has a duality gap Let the primal be sup : x 2 s.t. 2 4 x 2 0 0 0 x 1 x 2 0 x 2 0 3 5 2 4 ff 0 0 0 0 0 0 0 0 3 5 where ff 0. Then the LSD becomes: inf : ffU 11 s.t. U 22 = 0 U 11 2U 23 = 1 U 0 Any primal feasible solution has x 2 = 0, and hence ....
L. Vandenberghe, S. Boyd, Positive-Definite Programming, Mathematical Programming: State of the Art 1994, J.R. Birge and K.G. Murty ed.s, U. of Michigan, 1994.
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