课程名称︰凸函数最佳化
课程性质︰电机所选修
课程教师︰苏柏青
开课学院：电资学院
开课系所︰电机所
考试日期（年月日）︰108.06.20
考试时限（分钟）：100
试题 :
注：以下部分数学符号与式子以LaTeX语法表示。
1. (15%) Consider the convex unconstrained optimization problem whose variable
is x \in R^2:
minimize f_0(x) = [x_1 x_2][5 1 \\ 1 5][x_1 x_2].
We will study some types of descent methods in this problem.
(a) (3%) Find \nabla f_0, the gradient of f_0 for any x \in R^2.
(b) (4%) Find \nabla^2f_0, the Hessian of f_0 for any x \in R^2.
(c) (3%) Suppose the initial point is chosen to be x^{(0)} = [3 2]^T. Find the
gradient descent direction \Delta x_{gd}
(d) (5%) Again, let the initial point be x^{(0)} = [3 2]^T. Find the Newton st-
ep \Delta x_{nt}
2. (45%) Consider the convex piecewise-linear minimization problem
minimize \max_{i=1,...,m} (a_i^Tx + b_i)