## Which functions are convex?

A **convex function** is a continuous **function** whose value at the midpoint of every interval in its domain does not exceed the arithmetic mean of its values at the ends of the interval.

## How do you know if a function is convex?

A differentiable **function** of one variable is **convex** on an interval **if** and only **if** its derivative is monotonically non-decreasing on that interval. **If a function** is differentiable and **convex** then it is also continuously differentiable.

## How do you determine if a function is convex or concave?

For a twice-differentiable **function** f, **if** the second derivative, f ''(x), is positive (or, **if** the acceleration is positive), then the graph is **convex (or concave** upward); **if** the second derivative is negative, then the graph is **concave** (or **concave** downward).

## What is a convex loss function?

**Convex Loss** Functions. All of these are **convex** upper bounds on 0-1 **loss**. Hinge **loss**: L(y, y) = max{0, 1 − yy} Exponential **loss**: L(y, y) = exp(−yy) Logistic **loss**: L(y, y) = log2(1 + exp(−yy))

## Is logistic loss convex?

The method most commonly used for **logistic regression** is gradient descent. Gradient descent requires **convex** cost functions. Mean Squared Error, commonly used for linear **regression** models, isn't **convex** for **logistic regression**.

## What does it mean when a cost function is non convex?

The **cost function** of a neural network is in general neither **convex** nor **concave**. This **means** that the matrix of all second partial derivatives (the Hessian) is neither positive semidefinite, nor negative semidefinite. Since the second derivative is a matrix, it's possible that it's neither one or the other.

## What is convex cost function?

A **convex function**: given any two points on the curve there will be no intersection with any other points, for non **convex function** there will be at least one intersection. In terms of **cost function** with a **convex** type you are always guaranteed to have a global minimum, whilst for a non **convex** only local minima.

## What is convex set with example?

Equivalently, a **convex set** or a **convex** region is a subset that intersect every line into a single line segment (possibly empty). For **example**, a solid cube is a **convex set**, but anything that is hollow or has an indent, for **example**, a crescent shape, is not **convex**.

## What is convex objective function?

A **convex** optimization problem is a problem where all of the constraints are **convex functions**, and the **objective** is a **convex function** if minimizing, or a concave **function** if maximizing. ... With a **convex objective** and a **convex** feasible region, there can be only one optimal solution, which is globally optimal.

## What convex means?

**Definition** of **Convex** A **convex** shape **is** the opposite of a concave shape. ... Just like concave, **convex** can be used as a noun for a surface or line that curves outward, and it also has a use in geometry, where it describes a polygon with interior angles less than or equal to 180°.

## Why convex optimization is important?

6 Answers. Machine learning algorithms use **optimization** all the time. ... Nonetheless, as mentioned in other answers, **convex optimization** is faster, simpler and less computationally intensive, so it is often easier to "convexify" a problem (make it **convex optimization** friendly), then use non-**convex optimization**.

## Is e x convex?

The function **ex** is differentiable, and its second derivative **is ex** > 0, so that it is (strictly) **convex**.

## What is another word for Convex?

**Convex Synonyms** - WordHippo **Thesaurus**....**What is another word for convex**?

bulging | gibbous |
---|---|

outcurved | protuberant |

rounded | cambered |

swelling | arched |

bent | biconvex |

## What is a strongly convex function?

Intuitively speaking, **strong convexity** means that there exists a quadratic lower bound on the growth of the **function**. This directly implies that a **strong convex function** is **strictly convex** since the quadratic lower bound growth is of course **strictly** grater than the linear growth.

## Is log a convex function?

, the composition of the **logarithm** with f, is itself a **convex function**.

## Is log a concave function?

A **function** f(x) **is log concave** if **log**( f(x) ) is **concave**. The basic properties of convex functions are obvious. It's easy to show that the sum of two convex functions is convex, the maximum of two convex functions is convex, etc.

## Is entropy a convex function?

1.

## Is xy a convex function?

And since convexity has iff relation with H being positive semi-definite (i.e., all eigenvalues greater than or equal to zero) , we can say that the **xy** is neither **convex** nor concave. Consider the values of f at (1,3),(2,2),(3,1) and also at (1,1),(2,2),(3,3).

## Is a triangle convex?

A **convex** polygon is defined as a polygon with all its interior angles less than 180°. ... Note that a **triangle** (3-gon) is always **convex**. A **convex** polygon is the opposite of a concave polygon. See Concave Polygon.

## Is a sum of convex functions convex?

If f(x) is **convex**, then g(x) = f(ax+b) is also **convex** for any constants a, b ∈ R. ... If f(x) and g(x) are **convex**, then their **sum** h(x) = f(x) + g(x) is **convex**.

## What is convex in science?

1. curving or bulging outwards. 2. (General Physics) physics having one or two surfaces curved or ground in the shape of a section of the exterior of a sphere, paraboloid, ellipsoid, etc: a **convex** lens.

## What are convex figures?

A planar polygon is **convex** if it contains all the line segments connecting any pair of its points. Thus, for example, a regular pentagon is **convex** (left **figure**), while an indented pentagon is not (right **figure**). A planar polygon that is not **convex** is said to be a concave polygon.

## What is convex and concave mirror?

What are **convex and concave mirrors**? If the inner side of the spherical **mirror** is reflecting, it is called a **concave mirror**. If the outer side of the spherical **mirror** is reflecting, it is called a **convex mirror**. Image. **Concave mirrors** can form inverted and real images and also virtual and erect images.

## What is difference between concave and convex lens?

A **concave lens** is thinner **in the** middle and thicker at the edges. A **convex lens** is thicker **in the** middle and thinner at the edges. Used **in the** camera, focus sunlight, overhead projector, projector microscope, simple telescope, magnifying glasses, etc. It is also used for the correction of the problem in long sight.

## Which lens is concave?

A **concave lens** is a **lens** that possesses at least one surface that curves inwards. It is a diverging **lens**, meaning that it spreads out light rays that have been refracted through it. A **concave lens** is thinner at its centre than at its edges, and is used to correct short-sightedness (myopia).

## Where is convex lens used?

**Convex lenses** are **used** in eyeglasses for correcting farsightedness, where the distance between the eye's **lens** and retina is too short, as a result of which the focal point lies behind the retina. Eyeglasses with **convex lenses** increase refraction, and accordingly reduce the focal length.

## What are the examples of convex lens?

**Some examples of objects with convex lenses in include:**

- Binoculars and telescopes.
- Cameras.
- Eye glasses.
- Flashlights.
- Lasers ( CD, DVD players)

## What devices use convex lenses?

**Uses Of Convex Lens**

**Magnifying glasses**.**Eyeglasses**.**Cameras**.**Microscopes**.

## Which is convex lens?

A **convex lens** is also known as a **converging lens**. A **converging lens** is a **lens** that converges rays of light that are traveling parallel to its principal axis. They can be identified by their shape which is relatively thick across the middle and thin at the upper and lower edges.

## What is convex lens formula?

1. What is the **Lens Formula** for **Convex Lens**? Ans. According to the **convex lens equation**, 1/f = 1/v + 1/u. It relates the focal length of a **lens** with the distance of an object placed in front of it and the image formed of that object.

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