Consider minimizing a convex smooth function of one scalar variable, f). We guess an initial point...

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Consider minimizing a convex smooth function of one scalar variable, f). We guess an initial point (0), and take a second order Taylor expansion around (0). f(ß)f(30))+(3-3(0)) ( df where d 1 | B= B(0) = f'( 3 (0)) (hint: take derivative w.r.t. p) d f and d dw B=3(⁰) B=3(⁰) Show that to minimize the right-hand side, the next value of ß to guess is: f'(B(0)) 3(1) 3(0) f"(B(0)) 4/3=18(²) = f'" (B(0) 1 + + 2/7 ( B - 18(01) ²2 d²5 | dw² Consider minimizing a convex smooth function of one scalar variable, f). We guess an initial point (0), and take a second order Taylor expansion around (0). f(ß)f(30))+(3-3(0)) ( df where d 1 | B= B(0) = f'( 3 (0)) (hint: take derivative w.r.t. p) d f and d dw B=3(⁰) B=3(⁰) Show that to minimize the right-hand side, the next value of ß to guess is: f'(B(0)) 3(1) 3(0) f"(B(0)) 4/3=18(²) = f'" (B(0) 1 + + 2/7 ( B - 18(01) ²2 d²5 | dw²

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