Research any topic before you write.

Find related topics. | Discover entities. | See connections. | Build a topical map.

Convex function

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 of the function 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. In simple terms, a convex…

Properties, Overview & Strongly convex functions

Use the mouse wheel or two fingers (on touchscreens) to zoom in and out of the map.

Research this topic

Explore the main themes, entities and connections around Convex function. Start with the topic map, then use the sections below for research and deeper semantic analysis.

Explore this topic

Start with a few of the strongest sections from the source topic. These are research directions, not a list of keywords you must use.

Topics to explore

Browse the full topic structure. Each item opens a new analysis centered on that subject.

Overview

Definition

Properties

Functions of one variable

Operations that preserve convexity

Strongly convex functions

Examples

Advanced semantic analysis

Deeper signals for content research, entity SEO and topical coverage. The plain-language headings explain what each technical view is useful for.

Map overview Semantic statistics

Convex function

Nodes81
Edges80
Triples117
Avg. degree1.98
Density0.024691
Components1

How this topic connects Entity context

See the strongest relationship patterns around the current topic before diving into the raw triples.

Convex function

Top relations

related to References · 56
Convex function → Academic Press, Addison-Wesley, Adrian, Athena Scientific, Berlin, Bertsekas, Borwein, Brian, Claude, Convex, Convex Analysis, Convex Functions, CRC Press, David, Dimitri, Distributions, Donoghue, Fourier Transforms, Fundamentals, Groningen
related to Functions of one variable · 15
Convex function → As, Examples, For, From, If, In, It, More, Moreover, Namely, Since, Suppose, The, This, Visually
related to Operations that preserve convexity · 15
Convex function → Ax, Composition, Convexity, Danskin's, Dom, Elementwise, For, If, Important, In, Let, Minimization, Nonnegative, The, Then
related to Functions of several variables · 7
Convex function → Any, Consequently, For, Hessian, If, Indeed, Jensen's
related to External links · 4
Convex function → Convex, EMS Press, Encyclopedia, Mathematics
related to Functions of n variables · 4
Convex function → Every, LogSumExp, The, This
related to Properties of strongly-convex functions · 4
Convex function → For, If, Rn, The
related to Strongly convex functions · 3
Convex function → If, Intuitively, The
see also · 3
Convex function → Banach, Concave, Hadamard
related to Properties · 2
Convex function → Many, See

Important terminology Word statistics

Use these terms to understand the vocabulary surrounding the topic, not as a checklist for keyword stuffing.

Important terminology

convex displaystyle function functions real strictly domain variable strongly differentiable points derivative geq one concave leq line convexity f'' second

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Convex functionis afunction that grows as fast as a quadratic function0.90text
the arithmeticinstance ofcan be used to deduce inequalities0.80text
Convex functionrelated to External linksConvex0.60section
Convex functionrelated to External linksEncyclopedia0.60section
Convex functionrelated to External linksMathematics0.60section
Convex functionrelated to External linksEMS Press0.60section
Convex functionrelated to Functions of n variablesLogSumExp0.60section
Convex functionrelated to Functions of n variablesThe0.60section
Convex functionrelated to Functions of n variablesEvery0.60section
Convex functionrelated to Functions of n variablesThis0.60section
Convex functionrelated to Functions of one variableSuppose0.60section
Convex functionrelated to Functions of one variableThis0.60section

Related concept clusters Concept neighborhoods

These clusters group vocabulary that occurs around closely connected concepts in the source material.

    Connections between topic areas Semantic bridges

    Bridges can reveal useful research angles that are easy to miss in a flat list of related terms.

    Min side: 3
    For writers, content strategists, SEOs, marketers and creators — from quick topic research to advanced semantic analysis.