On maximization of quadratic form over intersection of ellipsoids with common center

On maximization of quadratic form over intersection of ellipsoids with common center

We demonstrate that if A1, ..., Am are symmetric positive semidefinite n×n matrices with positive definite sum and A is an arbitrary symmetric n×n matrix, then the relative accuracy, in terms of the optimal value, of the semidefinite relaxation max X {Tr(AX) | Tr(AiX) ≤ 1, i = 1, ...,m; X 0} (SDP) of the optimization program xTAx→ max | xAix ≤ 1, i = 1, ...,m (P) is not worse than 1 − 1 2 ln(2m...

On Maximization of Quadratic formover Intersection of Ellipsoids withCommon

We demonstrate that if A1; :::; Am are symmetric positive semide nite n n matrices with positive de nite sum and A is an arbitrary symmetric n n matrix, then the quality of the semide nite relaxation max X fTr(AX) j Tr(AiX) 1; i = 1; :::;m; X 0g (SDP) of the optimization program xTAx! max j xTAix 1; i = 1; :::;m (P) is not worse than 1 2 ln(2m2) . It is shown that this bound is sharp in order, ...

On Maximization of Quadratic formover Intersection of Ellipsoids

We demonstrate that if A1; :::; Am are symmetric positive semide nite n n matrices with positive de nite sum and A is an arbitrary symmetric n n matrix, then the quality of the semide nite relaxation max X fTr(AX) j Tr(AiX) 1; i = 1; :::;m; X 0g (SDP) of the optimization program xTAx! max j xTAix 1; i = 1; :::;m (P) is not worse than 1 2 ln(2m2) . It is shown that this bound is sharp in order, ...

Intersection of Ellipsoids

effect of oral presentation on development of l2 learners grammar

this experimental study has been conducted to test the effect of oral presentation on the development of l2 learners grammar. but this oral presentation is not merely a deductive instruction of grammatical points, in this presentation two hypotheses of krashen (input and low filter hypotheses), stevicks viewpoints on grammar explanation and correction and widdowsons opinion on limited use of l1...