V2EX convexity

Convexity

释义 Definition

凸性;凸性性质:指几何形状向外鼓起(相对于“凹”),更常见于数学与优化中,表示集合或函数满足“任取两点连线仍在内部/函数图像在连线之下”等性质。该词在数学语境最常用。

发音 Pronunciation (IPA)

/knvksti/

例句 Examples

Convexity is important in optimization.
凸性在优化问题中很重要。

The convexity of the loss function guarantees that any local minimum is also a global minimum.
损失函数的凸性保证了任何局部最小值同时也是全局最小值。

词源 Etymology

convexity 来自形容词 convex(“凸的”)加名词后缀 -ity(表示“性质、状态”)。convex 源自拉丁语 convexus,意为“拱起的、向外弯的”,与 *con-*(一起)和 *vex-/veh-*(弯曲、倾斜相关的词根)有关,整体表达“向外弯起的形态/性质”。

相关词 Related Words

文学与经典作品 Literary Works

  • Convex Optimization Stephen Boyd & Lieven Vandenberghe
  • Convex Analysis R. Tyrrell Rockafellar
  • Introductory Lectures on Convex Optimization: A Basic Course Yurii Nesterov
  • Nonlinear Programming Dimitri P. Bertsekas
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