Question: 1. Consider the steepest descent algorithm with an exact line search via or = arg minf (a* + adk) with dk = -Vf (ack ).

1. Consider the steepest descent algorithm with an exact line search via or = arg minf (a* + adk) with dk = -Vf (ack ). (a) Let a* denote the minimizer of the function h(a) := f(ack + adk ). Show that (dk, Vf (ack + akidk) ) = 0. (b) Now suppose that * and x* are two consecutive points generated by the steep- est descent algorithm with an exact line search as introduced in the beginning of this problem. Show that (Vf (ack ) , Vf (ack + 1 ) ) = 0

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