Convex Optimization · Problem 10.14

Interior-point methods — Boyd & Vandenberghe

Mathematics — Optimization · log-optimal-investment-newton

Problem

Log-optimal investment. Consider the log-optimal investment problem described in exercise 4.60, without the constraint x⪰0x \succeq 0. Use Newton's method to compute the solution, with the following problem data: there are n=3n = 3 assets, and m=4m = 4 scenarios, with returns p1=[21.31],p2=[20.51],p3=[0.51.31],p4=[0.50.51].p_1 = \begin{bmatrix} 2 \\ 1.3 \\ 1 \end{bmatrix}, \quad p_2 = \begin{bmatrix} 2 \\ 0.5 \\ 1 \end{bmatrix}, \quad p_3 = \begin{bmatrix} 0.5 \\ 1.3 \\ 1 \end{bmatrix}, \quad p_4 = \begin{bmatrix} 0.5 \\ 0.5 \\ 1 \end{bmatrix}. The probabilities of the four scenarios are given by π=(1/3,1/6,1/3,1/6)\pi = (1/3, 1/6, 1/3, 1/6).

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