Lectures 9 and 10 Lecturer : Michel

نویسنده

  • Michel X. Goemans
چکیده

1 Semidefinite programming Let Sn×n be the set of n by n real symmetric matrices. Definition 1 A ∈ Sn×n is called positive semidefinite, denoted A 0, if xAx ≥ 0 for any x ∈ R. There are several well-known equivalent ways to state positive semidefiniteness. Proposition 1 The following are equivalent: (i) A is positive semidefinite. (ii) Every eigenvalue of A is nonnegative. (iii) There is a matrix V such that A = V V . We define the Frobenius inner product for two matrices A,B ∈ Sn×n by 〈A,B〉 = ∑

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تاریخ انتشار 2014