Convex analysis | Generalized convexity | Types of functions
In mathematics, a real-valued function is called convex if the line segment between any two points on the graph of the function lies above 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. A twice-differentiable function of a single variable is convex if and only if its second derivative is nonnegative on its entire domain. Well-known examples of convex functions of a single variable include the quadratic function and the exponential function . In simple terms, a convex function refers to a function whose graph is shaped like a cup , while a concave function's graph is shaped like a cap . Convex functions play an important role in many areas of mathematics. They are especially important in the study of optimization problems where they are distinguished by a number of convenient properties. For instance, a strictly convex function on an open set has no more than one minimum. Even in infinite-dimensional spaces, under suitable additional hypotheses, convex functions continue to satisfy such properties and as a result, they are the most well-understood functionals in the calculus of variations. In probability theory, a convex function applied to the expected value of a random variable is always bounded above by the expected value of the convex function of the random variable. This result, known as Jensen's inequality, can be used to deduce inequalities such as the arithmetic–geometric mean inequality and Hölder's inequality. (Wikipedia).
Define linear functions. Use function notation to evaluate linear functions. Learn to identify linear function from data, graphs, and equations.
From playlist Algebra 1
Define a linear function. Determine if a linear function is increasing or decreasing. Interpret linear function models. Determine linear functions. Site: http://mathispower4u.com
From playlist Introduction to Functions: Function Basics
What are bounded functions and how do you determine the boundness
👉 Learn about the characteristics of a function. Given a function, we can determine the characteristics of the function's graph. We can determine the end behavior of the graph of the function (rises or falls left and rises or falls right). We can determine the number of zeros of the functi
From playlist Characteristics of Functions
Define an inverse function. Determine if a function as an inverse function. Determine inverse functions.
From playlist Determining Inverse Functions
(New Version Available) Inverse Functions
New Version: https://youtu.be/q6y0ToEhT1E Define an inverse function. Determine if a function as an inverse function. Determine inverse functions. http://mathispower4u.wordpress.com/
From playlist Exponential and Logarithmic Expressions and Equations
Introduction to Linear Functions and Slope (L10.1)
This lesson introduces linear functions, describes the behavior of linear function, and explains how to determine the slope of a line given two points. Video content created by Jenifer Bohart, William Meacham, Judy Sutor, and Donna Guhse from SCC (CC-BY 4.0)
From playlist Introduction to Functions: Function Basics
When is a function bounded below?
👉 Learn about the characteristics of a function. Given a function, we can determine the characteristics of the function's graph. We can determine the end behavior of the graph of the function (rises or falls left and rises or falls right). We can determine the number of zeros of the functi
From playlist Characteristics of Functions
Kazuo Murota: Extensions and Ramifications of Discrete Convexity Concepts
Submodular functions are widely recognized as a discrete analogue of convex functions. This convexity view of submodularity was established in the early 1980's by the fundamental works of A. Frank, S. Fujishige and L. Lovasz. Discrete convex analysis extends this view to broader classes of
From playlist HIM Lectures 2015
Ex: Determine if a Linear Function is Increasing or Decreasing
This video explains how to determine if a linear function is increasing or decreasing. The results are discussed graphically. Site: http://mathispower4u.com
From playlist Introduction to Functions: Function Basics
Lecture 4 | Convex Optimization I (Stanford)
Professor Stephen Boyd, of the Stanford University Electrical Engineering department, continues his lecture on convex functions in electrical engineering for the course, Convex Optimization I (EE 364A). Complete Playlist for the Course: http://www.youtube.com/view_play_list?p=3940DD956
From playlist Lecture Collection | Convex Optimization
Lecture 3 | Convex Optimization I (Stanford)
Professor Stephen Boyd, of the Stanford University Electrical Engineering department, lectures on convex and concave functions for the course, Convex Optimization I (EE 364A). Convex Optimization I concentrates on recognizing and solving convex optimization problems that arise in engine
From playlist Lecture Collection | Convex Optimization
Kazuo Murota: Discrete Convex Analysis (Part 2)
The lecture was held within the framework of the Hausdorff Trimester Program: Combinatorial Optimization
From playlist HIM Lectures 2015
Kazuo Murota: Discrete Convex Analysis (Part 3)
The lecture was held within the framework of the Hausdorff Trimester Program: Combinatorial Optimization
From playlist HIM Lectures 2015
Convexity and The Principle of Duality
A gentle and visual introduction to the topic of Convex Optimization (part 2/3). In this video, we give the definition of convex sets, convex functions, and convex optimization problems. We also present a beautiful and extremely useful notion in convexity optimization, which is the princ
From playlist Convex Optimization
Lecture 21: Minimizing a Function Step by Step
MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018 Instructor: Gilbert Strang View the complete course: https://ocw.mit.edu/18-065S18 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP63oMNUHXqIUcrkS2PivhN3k In this lecture, P
From playlist MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018
Beyond Convex for Global Optimization
In the field of optimization, convex optimization holds special status because of its property that the minimum is always a global minimum and there are highly efficient solvers available to solve convex problems. However, not all optimization problems can be formulated as purely convex pr
From playlist Wolfram Technology Conference 2021
Suvrit Sra: Lecture series on Aspects of Convex, Nonconvex, and Geometric Optimization (Lecture 3)
The lecture was held within the framework of the Hausdorff Trimester Program "Mathematics of Signal Processing". (28.1.2016)
From playlist HIM Lectures: Trimester Program "Mathematics of Signal Processing"
👉 Learn about the characteristics of a function. Given a function, we can determine the characteristics of the function's graph. We can determine the end behavior of the graph of the function (rises or falls left and rises or falls right). We can determine the number of zeros of the functi
From playlist Characteristics of Functions
👉 Learn about the characteristics of a function. Given a function, we can determine the characteristics of the function's graph. We can determine the end behavior of the graph of the function (rises or falls left and rises or falls right). We can determine the number of zeros of the functi
From playlist Characteristics of Functions
An Introduction to Geodesic Convexity - Nisheeth Vishnoi
Optimization, Complexity and Invariant Theory Topic: An Introduction to Geodesic Convexity Speaker: Nisheeth Vishnoi Affiliation: EPFL Date: June 7. 2018 For more videos, please visit http://video.ias.edu
From playlist Mathematics