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 less than or equal to the expected value of the convex function of the random variable. This result, known as Jensen's inequality, underlies many important inequalities (including, for instance, the arithmetic–geometric mean inequality and Hölder's inequality).
In this video I break down the formal definition of a concave function and attempt to explain all aspects and variables used in the definition. Being that a convex function is just the opposite in terms of its definition, once one of them is well understood the other is also understood.
If anyone has any questions or is still unsure on any concepts covered in the vid put them in the comment section and il try my best to answer.
published: 18 Oct 2020
17 - Convex functions
published: 22 Mar 2015
Convex problems
This video is part of the Udacity course "Machine Learning for Trading". Watch the full course at https://www.udacity.com/course/ud501
published: 01 Jul 2015
Convex and Concave Functions
For the book, you may refer: https://amzn.to/3aT4ino
This lecture explains how to check whether the function is convex or concave.
Other lectures:
Quadratic form: https://youtu.be/6jjTLDX_JOk
Hessian Matrix: https://youtu.be/mJB-XLV0QJc
Convex & Concave function: https://youtu.be/nZ7vjo2dQ1o
Maxima & Minima of the function: https://youtu.be/gJHgIcMeS2M
published: 01 Apr 2021
Convex functions and Jensen's inequality
"(1) Convex functions
(2) Jensen's inequality
(3) Use of Jensen's inequality in the MLE of GMMs"
published: 14 Sep 2022
Operations Research 03F: Convex Set & Convex Function
Textbooks:
https://amzn.to/2VgimyJ
https://amzn.to/2CHalvx
https://amzn.to/2Svk11k
In this video, I'll talk about some concepts such as convex combinations, convex sets, convex functions, and concave functions.
----------------------------------------
Smart Energy Operations Research Lab (SEORL): http://binghamton.edu/seorl
YOUTUBE CHANNEL: http://youtube.com/yongtwan
published: 19 Mar 2017
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 principle duality.
This is the second video of the series.
Part 1: What is (Mathematical) Optimization? (https://youtu.be/AM6BY4btj-M)
Part 2: Convexity and the Principle of (Lagrangian) Duality (https://youtu.be/d0CF3d5aEGc)
Part 3: Algorithms for Convex Optimization (Interior Point Methods). (https://youtu.be/uh1Dk68cfWs)
Typos:
- At 7:59, there is an extra minus sign in the right hand side of the equation A^TAx = -A^Tb. The correct equation is A^TAx = A^Tb,which leads to the solution x = (A^TA)^-1 A^...
published: 15 Jul 2021
Lecture 17(B): Concave and Convex Functions
Extended utility function example. Monotone transform. Quasiconcave and quasiconvex functions. Characterization in terms of convex upper and lower contour sets.
published: 04 Jun 2020
Refraction from Rarer to Denser for Convex Spherical Surface #rayoptics #class12 #physics
Refraction from Rarer to Denser for Convex Spherical Surface #rayoptics #class12 #physics
published: 28 Dec 2023
Lecture 2 | Convex Optimization I (Stanford)
Guest Lecturer Jacob Mattingley covers convex sets and their applications in electrical engineering and beyond for the course, Convex Optimization I (EE 364A).
Convex Optimization I concentrates on recognizing and solving convex optimization problems that arise in engineering. Convex sets, functions, and optimization problems. Basics of convex analysis. Least-squares, linear and quadratic programs, semidefinite programming, minimax, extremal volume, and other problems. Optimality conditions, duality theory, theorems of alternative, and applications. Interior-point methods. Applications to signal processing, control, digital and analog circuit design, computational geometry, statistics, and mechanical engineering.
Complete Playlist for the Course:
http://www.youtube.com/view_play_lis...
In this video I break down the formal definition of a concave function and attempt to explain all aspects and variables used in the definition. Being that a con...
In this video I break down the formal definition of a concave function and attempt to explain all aspects and variables used in the definition. Being that a convex function is just the opposite in terms of its definition, once one of them is well understood the other is also understood.
If anyone has any questions or is still unsure on any concepts covered in the vid put them in the comment section and il try my best to answer.
In this video I break down the formal definition of a concave function and attempt to explain all aspects and variables used in the definition. Being that a convex function is just the opposite in terms of its definition, once one of them is well understood the other is also understood.
If anyone has any questions or is still unsure on any concepts covered in the vid put them in the comment section and il try my best to answer.
For the book, you may refer: https://amzn.to/3aT4ino
This lecture explains how to check whether the function is convex or concave.
Other lectures:
Quadratic f...
For the book, you may refer: https://amzn.to/3aT4ino
This lecture explains how to check whether the function is convex or concave.
Other lectures:
Quadratic form: https://youtu.be/6jjTLDX_JOk
Hessian Matrix: https://youtu.be/mJB-XLV0QJc
Convex & Concave function: https://youtu.be/nZ7vjo2dQ1o
Maxima & Minima of the function: https://youtu.be/gJHgIcMeS2M
For the book, you may refer: https://amzn.to/3aT4ino
This lecture explains how to check whether the function is convex or concave.
Other lectures:
Quadratic form: https://youtu.be/6jjTLDX_JOk
Hessian Matrix: https://youtu.be/mJB-XLV0QJc
Convex & Concave function: https://youtu.be/nZ7vjo2dQ1o
Maxima & Minima of the function: https://youtu.be/gJHgIcMeS2M
Textbooks:
https://amzn.to/2VgimyJ
https://amzn.to/2CHalvx
https://amzn.to/2Svk11k
In this video, I'll talk about some concepts such as convex combinations, c...
Textbooks:
https://amzn.to/2VgimyJ
https://amzn.to/2CHalvx
https://amzn.to/2Svk11k
In this video, I'll talk about some concepts such as convex combinations, convex sets, convex functions, and concave functions.
----------------------------------------
Smart Energy Operations Research Lab (SEORL): http://binghamton.edu/seorl
YOUTUBE CHANNEL: http://youtube.com/yongtwan
Textbooks:
https://amzn.to/2VgimyJ
https://amzn.to/2CHalvx
https://amzn.to/2Svk11k
In this video, I'll talk about some concepts such as convex combinations, convex sets, convex functions, and concave functions.
----------------------------------------
Smart Energy Operations Research Lab (SEORL): http://binghamton.edu/seorl
YOUTUBE CHANNEL: http://youtube.com/yongtwan
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 co...
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 principle duality.
This is the second video of the series.
Part 1: What is (Mathematical) Optimization? (https://youtu.be/AM6BY4btj-M)
Part 2: Convexity and the Principle of (Lagrangian) Duality (https://youtu.be/d0CF3d5aEGc)
Part 3: Algorithms for Convex Optimization (Interior Point Methods). (https://youtu.be/uh1Dk68cfWs)
Typos:
- At 7:59, there is an extra minus sign in the right hand side of the equation A^TAx = -A^Tb. The correct equation is A^TAx = A^Tb,which leads to the solution x = (A^TA)^-1 A^T b.
--------------------------------
Timestamps:
0:00 Previously
1:00 Definition of Convex Sets
1:47 Definition of Convex Functions
2:45 Definition of Convex Optimization Problems
3:36 Duality for Convex Sets
6:09 Duality for Convex Functions
8:40 Examples
--------------------------
Credit:
🐍 Manim and Python : https://github.com/3b1b/manim
🐵 Blender3D: https://www.blender.org/
🗒️ Emacs: https://www.gnu.org/software/emacs/
This video would not have been possible without the help of Gökçe Dayanıklı.
--------------------------
🎵 Music
- Vincent Rubinetti (https://vincerubinetti.bandcamp.com/)
- Carefree by Kevin MacLeod (https://www.youtube.com/watch?v=8SIrVXr9hjA)
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 principle duality.
This is the second video of the series.
Part 1: What is (Mathematical) Optimization? (https://youtu.be/AM6BY4btj-M)
Part 2: Convexity and the Principle of (Lagrangian) Duality (https://youtu.be/d0CF3d5aEGc)
Part 3: Algorithms for Convex Optimization (Interior Point Methods). (https://youtu.be/uh1Dk68cfWs)
Typos:
- At 7:59, there is an extra minus sign in the right hand side of the equation A^TAx = -A^Tb. The correct equation is A^TAx = A^Tb,which leads to the solution x = (A^TA)^-1 A^T b.
--------------------------------
Timestamps:
0:00 Previously
1:00 Definition of Convex Sets
1:47 Definition of Convex Functions
2:45 Definition of Convex Optimization Problems
3:36 Duality for Convex Sets
6:09 Duality for Convex Functions
8:40 Examples
--------------------------
Credit:
🐍 Manim and Python : https://github.com/3b1b/manim
🐵 Blender3D: https://www.blender.org/
🗒️ Emacs: https://www.gnu.org/software/emacs/
This video would not have been possible without the help of Gökçe Dayanıklı.
--------------------------
🎵 Music
- Vincent Rubinetti (https://vincerubinetti.bandcamp.com/)
- Carefree by Kevin MacLeod (https://www.youtube.com/watch?v=8SIrVXr9hjA)
Extended utility function example. Monotone transform. Quasiconcave and quasiconvex functions. Characterization in terms of convex upper and lower contour sets....
Extended utility function example. Monotone transform. Quasiconcave and quasiconvex functions. Characterization in terms of convex upper and lower contour sets.
Extended utility function example. Monotone transform. Quasiconcave and quasiconvex functions. Characterization in terms of convex upper and lower contour sets.
Guest Lecturer Jacob Mattingley covers convex sets and their applications in electrical engineering and beyond for the course, Convex Optimization I (EE 364A).
...
Guest Lecturer Jacob Mattingley covers convex sets and their applications in electrical engineering and beyond for the course, Convex Optimization I (EE 364A).
Convex Optimization I concentrates on recognizing and solving convex optimization problems that arise in engineering. Convex sets, functions, and optimization problems. Basics of convex analysis. Least-squares, linear and quadratic programs, semidefinite programming, minimax, extremal volume, and other problems. Optimality conditions, duality theory, theorems of alternative, and applications. Interior-point methods. Applications to signal processing, control, digital and analog circuit design, computational geometry, statistics, and mechanical engineering.
Complete Playlist for the Course:
http://www.youtube.com/view_play_list?p=3940DD956CDF0622
EE 364A Course Website:
http://www.stanford.edu/class/ee364
Stanford University:
http://www.stanford.edu/
Stanford University Channel on YouTube:
http://www.youtube.com/stanford/
Guest Lecturer Jacob Mattingley covers convex sets and their applications in electrical engineering and beyond for the course, Convex Optimization I (EE 364A).
Convex Optimization I concentrates on recognizing and solving convex optimization problems that arise in engineering. Convex sets, functions, and optimization problems. Basics of convex analysis. Least-squares, linear and quadratic programs, semidefinite programming, minimax, extremal volume, and other problems. Optimality conditions, duality theory, theorems of alternative, and applications. Interior-point methods. Applications to signal processing, control, digital and analog circuit design, computational geometry, statistics, and mechanical engineering.
Complete Playlist for the Course:
http://www.youtube.com/view_play_list?p=3940DD956CDF0622
EE 364A Course Website:
http://www.stanford.edu/class/ee364
Stanford University:
http://www.stanford.edu/
Stanford University Channel on YouTube:
http://www.youtube.com/stanford/
In this video I break down the formal definition of a concave function and attempt to explain all aspects and variables used in the definition. Being that a convex function is just the opposite in terms of its definition, once one of them is well understood the other is also understood.
If anyone has any questions or is still unsure on any concepts covered in the vid put them in the comment section and il try my best to answer.
For the book, you may refer: https://amzn.to/3aT4ino
This lecture explains how to check whether the function is convex or concave.
Other lectures:
Quadratic form: https://youtu.be/6jjTLDX_JOk
Hessian Matrix: https://youtu.be/mJB-XLV0QJc
Convex & Concave function: https://youtu.be/nZ7vjo2dQ1o
Maxima & Minima of the function: https://youtu.be/gJHgIcMeS2M
Textbooks:
https://amzn.to/2VgimyJ
https://amzn.to/2CHalvx
https://amzn.to/2Svk11k
In this video, I'll talk about some concepts such as convex combinations, convex sets, convex functions, and concave functions.
----------------------------------------
Smart Energy Operations Research Lab (SEORL): http://binghamton.edu/seorl
YOUTUBE CHANNEL: http://youtube.com/yongtwan
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 principle duality.
This is the second video of the series.
Part 1: What is (Mathematical) Optimization? (https://youtu.be/AM6BY4btj-M)
Part 2: Convexity and the Principle of (Lagrangian) Duality (https://youtu.be/d0CF3d5aEGc)
Part 3: Algorithms for Convex Optimization (Interior Point Methods). (https://youtu.be/uh1Dk68cfWs)
Typos:
- At 7:59, there is an extra minus sign in the right hand side of the equation A^TAx = -A^Tb. The correct equation is A^TAx = A^Tb,which leads to the solution x = (A^TA)^-1 A^T b.
--------------------------------
Timestamps:
0:00 Previously
1:00 Definition of Convex Sets
1:47 Definition of Convex Functions
2:45 Definition of Convex Optimization Problems
3:36 Duality for Convex Sets
6:09 Duality for Convex Functions
8:40 Examples
--------------------------
Credit:
🐍 Manim and Python : https://github.com/3b1b/manim
🐵 Blender3D: https://www.blender.org/
🗒️ Emacs: https://www.gnu.org/software/emacs/
This video would not have been possible without the help of Gökçe Dayanıklı.
--------------------------
🎵 Music
- Vincent Rubinetti (https://vincerubinetti.bandcamp.com/)
- Carefree by Kevin MacLeod (https://www.youtube.com/watch?v=8SIrVXr9hjA)
Extended utility function example. Monotone transform. Quasiconcave and quasiconvex functions. Characterization in terms of convex upper and lower contour sets.
Guest Lecturer Jacob Mattingley covers convex sets and their applications in electrical engineering and beyond for the course, Convex Optimization I (EE 364A).
Convex Optimization I concentrates on recognizing and solving convex optimization problems that arise in engineering. Convex sets, functions, and optimization problems. Basics of convex analysis. Least-squares, linear and quadratic programs, semidefinite programming, minimax, extremal volume, and other problems. Optimality conditions, duality theory, theorems of alternative, and applications. Interior-point methods. Applications to signal processing, control, digital and analog circuit design, computational geometry, statistics, and mechanical engineering.
Complete Playlist for the Course:
http://www.youtube.com/view_play_list?p=3940DD956CDF0622
EE 364A Course Website:
http://www.stanford.edu/class/ee364
Stanford University:
http://www.stanford.edu/
Stanford University Channel on YouTube:
http://www.youtube.com/stanford/
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 less than or equal to the expected value of the convex function of the random variable. This result, known as Jensen's inequality, underlies many important inequalities (including, for instance, the arithmetic–geometric mean inequality and Hölder's inequality).
When a water-filled container is placed over an object, the curved surface of the water functions as a convex lens, causing light rays passing through it to converge and create a magnified image of the object below.
Sturdy and Fashionable design Stable and Adjustable with 360-degree functionClearVision with 6.7inch large convex lens EasyInstallation with included accessories Compatible with various vehicles.
From sleek modern designs to vintage-inspired classics, these clocks not only function as practical time tellers but also serve as stunning decorative elements for any room ... beauty and functionality.
Overall, this wall clock offers functionality, style, and durability ... With easy viewing from any angle and a sturdy plastic frame with spherical convex glass lens, this clock is both functional and stylish.
ConvexMirrorVaseSilver Cubicle Decorations ... The Skywin Convex Mirror Vase is a functional and stylish addition to any office or living space ... Enhance your office or home with the Skywin Convex Mirror Vase and enjoy its multipurpose functionality.
Improve your cooking experience with AGARO's perfect blend of form and function... Serrated, Convex, Fine, StraightItem Dimensions ... This multi-functional marvel seamlessly combines the efficiency of a vegetable cutter and slicer ... 2 in 1 functionality.
... including the theory of self-concordant functions and interior-point methods, a complexity theory of optimization, accelerated gradient methods, and methodological advances in robust optimization.".
With its unbreakable convex lens and 360-degree rotation, you can easily adjust the mirror for the perfect angle, boosting your confidence on the road ... With a customer rating of 4.4 out of 5, this bike mirror offers great value and functionality.
It involves finding the minimum of a convex function subject to constraints ...Convex optimization works by finding the ... It involves finding the minimum of a convex function subject to constraints.
the ability to read and write a range of new file formats, improvements to nesting capabilities, the introduction of convex hull generation, new functionality for ACIS Polyhedra, and a myriad of other improvements to Spatial’s components.
We've developed new key labels that clearly represent each feature and function, and there is a robust library of mathematical functions presented in app and catalog format." ... each scientific function.
Further to that very factor, all of the users will find themselves in the position of staking cvxCRV and obtaining CRV from the performance fee of Convex, together with the platform’s conventional token CVX.
and the 
for any real number x.
Enid News & Eagle
01 Nov 2023
Enid News & Eagle
01 Nov 2023