格里旺克函式

格里旺克函式（Griewank function）是數學上常用於測試最佳化程式效率的函式。

基本介紹

• 中文名：格里旺克函式
• 外文名：Griewank function
• 分類：特殊函式
• 套用：數字最佳化
• 領域：數理科學

定義

數學定義如下：

一階格里旺函式

如圖1所示，一階格里旺函式有許多極點。 取上述函式的一階導數，令其為0：

用數值解法，求其中在實數域[-100..100]之間的解，共得62個，列出如下：

圖1一階格里旺函式

[-97.438110610025603200, -94.200661844477748520, -91.151778636270389965, -87.920619819329359985, -84.865447114417916660, -81.640577359698817225, -78.579116013127494725, -75.360534496781834905, -72.292785301096032350, -69.080491261738200370, -66.006454947055212230, -62.800447685694571355, -59.720124919768677970, -56.520403799747265470, -53.433795188029228405, -50.240359634965042195, -47.147465720656019171, -43.960315222391878044, -40.861136486491770843, -37.680270593049735600, -34.574807454399982858, -31.400225777941327138, -28.288478593262152626, -25.120180808052873462, -22.002149871974999083, -18.840135714356858698, -15.715821259447690012, -12.560090527814781691, -9.4294927245990724370, -6.2800452793799046870, -3.1431642363549054240, 3.1431642363549054240, 6.2800452793799046870, 9.4294927245990724370, 12.560090527814781691, 15.715821259447690012, 18.840135714356858698, 22.002149871974999083, 25.120180808052873462, 28.288478593262152626, 31.400225777941327138, 34.574807454399982858, 37.680270593049735600, 40.861136486491770847, 43.960315222391878044, 47.147465720656019171, 50.240359634965042195, 53.433795188029228405, 56.520403799747265470, 59.720124919768677970, 62.800447685694571355, 66.006454947055212230, 69.080491261738200370, 72.292785301096032350, 75.360534496781834905, 78.579116013127494725, 81.640577359698817225, 84.865447114417916660, 87.920619819329359985, 91.151778636270389965, 94.200661844477748520, 97.438110610025603200, 0.]

在[-10000,10000]區間，極點個數=6365

二階格里旺函式

圖2二階格里旺函式

相關條目

• Himmelblau函式
  
• Rastrigin函式
  
• Rosenbrock函式