The class operations research, first introduced the planning algorithm for unconstrained nonlinear programming algorithm. Dichotomy and golden section is part of the representative of the one-dimensional search method for unconstrained programming algorithm.
Dichotomy: $$. 1} ^ {X_ {(. 1 + K)} = \ FRAC. 1} {2} {(R & lt X_ {} ^ {(K) + X_ {L}} ^ {(K)} - \ delta) $$$$ x_ {2} ^ {(k + 1)} = \ frac {1} {2} (x_ {R} ^ {(k)} + x_ {L} ^ {(k)} + \ Delta) $$
Golden Section: $$. 1} ^ {X_ {(. 1 + K)} = X_ {R & lt ^ {} (K)} - (\ FRAC {\ sqrt {-1}. 5} {2}) (R & lt X_ { } ^ {(k)} - x_ {L} ^ {(k)}) $$$$ x_ {2} ^ {(k + 1)} = x_ {L} ^ {(k)} + (\ frac {\ sqrt {5} -1} {2}) (x_ {R} ^ {(k)} - x_ {L} ^ {(k)}) $$
Selected $ x_ {1} ^ {(k + 1)} $ and $ x_ {2} ^ {(k + 1)} $ must meet $$ x_ {L} ^ {(k)} <x_ {1} ^ {(k + 1)} <x_ {2} ^ {(k + 1)} <x_ {R} ^ {(k)} $$
Implementation code dichotomy Golden Section and under the following recording by the Python.