V2EX convex optimization

Convex Optimization

Definition 定义

凸优化:一类优化问题,其中目标函数是凸函数、约束集合是凸集;因此通常具有全局最优解且更容易高效求解(如用内点法、梯度法等)。该术语也常泛指相关的理论与算法体系。

Pronunciation 发音

/knvks ptmzen/

Examples 例句

Convex optimization is widely used in machine learning.
凸优化广泛应用于机器学习中。

By formulating the portfolio selection as a convex optimization problem with risk constraints, we can guarantee a globally optimal solution under the model assumptions.
通过把投资组合选择表述为带风险约束的凸优化问题,在模型假设成立时我们可以保证得到全局最优解。

Etymology 词源

convex 源自拉丁语 convexus,意为“向外拱起的、凸的”,在数学中用来描述“连接任意两点的线段仍落在集合内”的性质(凸集/凸函数)。
optimization 来自 optimize(“使最优”),与拉丁语 optimus(“最好的”)同源;合起来表示“在凸性条件下进行最优化求解”的方法与问题类型。

Related Words 相关词

Literary Works 文学作品

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