Convex Optimization · Problem 2.28

Convex functions — Boyd & Vandenberghe

Mathematics — Optimization · positive-semidefinite-cone

Problem

Positive semidefinite cone for n=1,2,3n = 1, 2, 3. Give an explicit description of the positive semidefinite cone S+n\mathbf{S}^n_+, in terms of the matrix coefficients and ordinary inequalities, for n=1,2,3n = 1, 2, 3. To describe a general element of Sn\mathbf{S}^n, for n=1,2,3n = 1, 2, 3, use the notation x1,[x1x2x2x3],[x1x2x3x2x4x5x3x5x6].x_1, \qquad \begin{bmatrix} x_1 & x_2 \\ x_2 & x_3 \end{bmatrix}, \qquad \begin{bmatrix} x_1 & x_2 & x_3 \\ x_2 & x_4 & x_5 \\ x_3 & x_5 & x_6 \end{bmatrix}.

Browse the problem library