Convex analysis | Convex geometry
In geometry, a subset of a Euclidean space, or more generally an affine space over the reals, is convex if, given any two points in the subset, the subset contains the whole line segment that joins them. Equivalently, a convex set or a convex region is a subset that intersects 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. The boundary of a convex set is always a convex curve. The intersection of all the convex sets that contain a given subset A of Euclidean space is called the convex hull of A. It is the smallest convex set containing A. A convex function is a real-valued function defined on an interval with the property that its epigraph (the set of points on or above the graph of the function) is a convex set. Convex minimization is a subfield of optimization that studies the problem of minimizing convex functions over convex sets. The branch of mathematics devoted to the study of properties of convex sets and convex functions is called convex analysis. The notion of a convex set can be generalized as described below. (Wikipedia).
What is the difference between convex and concave
👉 Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons
Introduction to sets || Set theory Overview - Part 2
A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other #sets. The #set with no element is the empty
From playlist Set Theory
What is the difference between convex and concave polygons
👉 Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons
👉 Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons
Introduction to sets || Set theory Overview - Part 1
A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other #sets. The #set with no element is the empty
From playlist Set Theory
V3-32. Linear Programming. Convexity. Intersection of convex sets.
Math 484: Linear Programming. Convexity. Intersection of convex sets. Wen Shen, 2020, Penn State University
From playlist Math484 Linear Programming Short Videos, summer 2020
What is the difference between concave and convex polygons
👉 Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons
👉 Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons
👉 Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons
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 se
From playlist Lecture Collection | Convex Optimization
Linear Programming, Lecture 12. Convexity.
September 29, 2016. Penn State University.
From playlist Math484, Linear Programming, fall 2016
Mateusz Skomora: Separation theorems in signed tropical convexities
The max-plus semifield can be equipped with a natural notion of convexity called the “tropical convexity”. This convexity has many similarities with the standard convexity over the nonnegative real numbers. In particular, it has been shown that tropical polyhedra are closely related to the
From playlist Workshop: Tropical geometry and the geometry of linear programming
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
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
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
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
Matthew Kennedy: Noncommutative convexity
Talk by Matthew Kennedy in Global Noncommutative Geometry Seminar (Europe) http://www.noncommutativegeometry.nl/ncgseminar/ on May 5, 2021
From playlist Global Noncommutative Geometry Seminar (Europe)
Tropical Geometry - Lecture 9 - Tropical Convexity | Bernd Sturmfels
Twelve lectures on Tropical Geometry by Bernd Sturmfels (Max Planck Institute for Mathematics in the Sciences | Leipzig, Germany) We recommend supplementing these lectures by reading the book "Introduction to Tropical Geometry" (Maclagan, Sturmfels - 2015 - American Mathematical Society)
From playlist Twelve Lectures on Tropical Geometry by Bernd Sturmfels
Symplectic convexity? (an ongoing story...)
Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar Topic: Symplectic convexity? (an ongoing story...) Speaker: Jean Gutt Affiliation: University of Toulouse Date: October 21, 2022 What is the symplectic analogue of being convex? We shall present different ideas to
From playlist Mathematics
Introduction to Sets and Set Notation
This video defines a set, special sets, and set notation.
From playlist Sets (Discrete Math)