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1. Consider the following optimization problem min TER" 2 where A E Rmxn, b E RM, and B E RPX" are given. Find the steepest descent (i.e. gradient descent with the exact line search) algorithm for solving this optimization. In the following two problems, we consider variants of the gradient descent algorithm for solving min f(x), IER" (1) where f : R" - R is a smooth function. Given a (*), the gradient descent algorithm finds a(*+1) by ( *+)) = arg min f(x(")) + (Vf(x(1)), x - 2(*)) + 1 20* k (2) TER where ax > 0 is a step size