Y. Nesterov and A. Nemirovskii. Interior Point Polynomial Algorithms  Home/Search   Document Not in Database   Summary   Related Articles

....There exist finite primal and dual optimal solutions X and (y; Z) Assumption 3. The matrices A k ; k = 1; m, are linearly independent, i.e. they span an m dimensional linear space in S n . Semidefinite Programming 3 Assumption 1 (the Slater condition) and Assumption 2 imply (see e.g. [NN94]) that the duality gap X ffl Z = 0 for optimal solutions (X; y; Z) As is well known, this implies the complementary condition XZ = 0: 4) To prove this, observe that X 0, Z 0 and tr XZ = 0 imply that the matrix X 1=2 ZX 1=2 is symmetric, positive semidefinite, and has zero trace. It ....

Y. Nesterov and A. Nemirovskii. Interior Point Polynomial Algorithms

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC