Suppose K_1 and K_2 are positive definite n x n matrices. Suppose that, for i = 1,2, the minimizer of p_i(x) = x^(T)K_i(x) -2x^(T)f_i + c_i, is x^*. Is the minimizer of p(x) = p_1(x) + p_2(x) given by x^* = (x^*)_1 + (x^*)_2? Prove or give a counterexample.
How can I do this problem?
How can I do this problem?