Bài giảng Tối ưu hóa vận hành hệ thống điện - Chapter 2: Introduction to optimization - Võ Ngọc Điều

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Sufficient Conditions for Optimality

• Calculate the eigenvalues of the Hessian matrix

at the stationary point • If all the eigenvalues are greater or equal to zero:

. The matrix is positive semi-definite

. The stationary point is a minimum • If all the eigenvalues are less or equal to zero:

. The matrix is negative semi-definite

. The stationary point is a maximum • If some or the eigenvalues are positive and other

are negative: . The stationary point is a saddle point