凸函数（英文：Convex function）是指函数图形上，任意兩點連成的線段，皆位於圖形的上方的实值函数， [1] 如單變數的二次函数和指数函数。 二階可導的一元函數 f {\displaystyle f} 為凸， 当且仅当 其定義域為凸集，且函數的二階導數 f ″ {\displaystyle f''} 在整個定 ...

Convex is the open-source reactive database for app developers. From database schemas to queries, from auth to APIs, express every part of your backend in pure TypeScript. Your backend code lives next to your app code, is typechecked and autocompleted, and is generated by AI with exceptional accuracy.

2020年2月1日 · 最简单也是最直观的辨识方法是，如果曲线的凹凸部位位于两点连接的直线（即下图中的紫色线）下方，则为convex函数（如下图所示）。 如果曲线的凹凸部位位于两点连接的直线（下图中的紫色线）的上方，则为concave函数（如下图所示）。

In mathematics, a real-valued function is called convex if the line segment between any two distinct points on the graph of the function lies above or on the graph between the two points. Equivalently, a function is convex if its epigraph (the set of points on or above the graph of the function) is a convex set.

2021年7月13日 · Concave and convex are literal opposites—one involves shapes that curve inward and the other involves shapes that curve outward. The terms can be used generally, but they’re often used in technical, scientific, and geometric contexts.

2021年3月2日 · An object with a convex shape is one that curves outward, such as a basketball or a baseball. The middle is thicker than the edges. The words concave and convex describe the direction that an object curves. Because concave shapes curve in and convex shapes curve out, each of these two words describes opposite shapes.

2023年9月9日 · Concave lenses focus light inside the curve of the lens, while convex lenses focus light using the outer curve. A lens that curves like a “C” (no flat side) is both concave or convex, depending on which side of the lens you view from. Examples: Eyeglasses for nearsighted people, cameras, telescopic sights. Properties: Diverge light rays.

2020年4月7日 · convex（凸函数）指的是V形状的函数，concave（凹函数）指的是^形状的函数。 实际上，我们最好不要用凹函数这一说法，推行上凸和下凸（描述函数的凸性），都是凸函数。 不是凸函数的，就是非凸函。 在你心中，可以不记凹凸了，记得上凸、下凸是啥样即可。 图3. 凸函数. 判定方法：对于一元函数f (x)，我们可以通过其二阶导数f′′ (x) 的符号来判断。 如果函数的二阶导数总是非负，即f′′ (x)≥0 ，则f (x)是凸函数。 对于多元函数f (X)，我们可以通过其Hessian矩 …

2024年9月22日 · In this article, we will explore the key concepts of convex and concave functions, their mathematical properties, and how to identify and apply them in various fields. We'll also look at practical examples and graphical representations.

Convex is the open source, reactive database where queries are TypeScript code running right in the database. Just like React components react to state changes, Convex queries react to database changes. Convex provides a database, a place …