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z 1 2 + z 1 z 2 + 2z 2 2 + 3z 1 + z 2

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(1)

宿題

次の

2

変数

2

次関数

z 1 2 + z 1 z 2 + 2z 2 2 + 3z 1 + z 2

を最小化する

z 1 , z 2

を最急降下法により求めよ

.

なお

,

初期 パラメータは

z 1 = z 2 = 0

とする. 第

1

ステップおよび第

2

ステップのパラメータを小数点以下第

2

位まで求め

,

その軌 跡を以下に図示せよ.

-1.5 -1 -0.5 0 0.5 1 1.5 2

-4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1

z2

z1

Ichiro Takeuchi, Nagoya Institute of Technology 5/5

参照

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