Geometric algorithms | Linear programming | Convex optimization | P-complete problems
Linear programming (LP), also called linear optimization, is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships. Linear programming is a special case of mathematical programming (also known as mathematical optimization). More formally, linear programming is a technique for the optimization of a linear objective function, subject to linear equality and linear inequality constraints. Its feasible region is a convex polytope, which is a set defined as the intersection of finitely many half spaces, each of which is defined by a linear inequality. Its objective function is a real-valued affine (linear) function defined on this polyhedron. A linear programming algorithm finds a point in the polytope where this function has the smallest (or largest) value if such a point exists. Linear programs are problems that can be expressed in canonical form as Here the components of x are the variables to be determined, c and b are given vectors (with indicating that the coefficients of c are used as a single-row matrix for the purpose of forming the matrix product), and A is a given matrix. The function whose value is to be maximized or minimized ( in this case) is called the objective function. The inequalities Ax ≤ b and x ≥ 0 are the constraints which specify a convex polytope over which the objective function is to be optimized. In this context, two vectors are comparable when they have the same dimensions. If every entry in the first is less-than or equal-to the corresponding entry in the second, then it can be said that the first vector is less-than or equal-to the second vector. Linear programming can be applied to various fields of study. It is widely used in mathematics and, to a lesser extent, in business, economics, and some engineering problems. Industries that use linear programming models include transportation, energy, telecommunications, and manufacturing. It has proven useful in modeling diverse types of problems in planning, routing, scheduling, assignment, and design. (Wikipedia).
Powered by https://www.numerise.com/ Formulating a linear programming problem
From playlist Linear Programming - Decision Maths 1
👉 Learn about graphing linear equations. A linear equation is an equation whose highest exponent on its variable(s) is 1. i.e. linear equations has no exponents on their variables. The graph of a linear equation is a straight line. To graph a linear equation, we identify two values (x-valu
From playlist ⚡️Graph Linear Equations | Learn About
Define linear functions. Use function notation to evaluate linear functions. Learn to identify linear function from data, graphs, and equations.
From playlist Algebra 1
V6 01: Linear Programming: Introduction to Integer programming
Linear Programming: Introduction to Integer programming
From playlist Math484 Linear Programming Short Videos, summer 2020
What is the parent function of a linear graph
👉 Learn about graphing linear equations. A linear equation is an equation whose highest exponent on its variable(s) is 1. i.e. linear equations has no exponents on their variables. The graph of a linear equation is a straight line. To graph a linear equation, we identify two values (x-valu
From playlist ⚡️Graph Linear Equations | Learn About
👉 Learn about graphing linear equations. A linear equation is an equation whose highest exponent on its variable(s) is 1. i.e. linear equations has no exponents on their variables. The graph of a linear equation is a straight line. To graph a linear equation, we identify two values (x-valu
From playlist ⚡️Graph Linear Equations | Learn About
👉 Learn about graphing linear equations. A linear equation is an equation whose highest exponent on its variable(s) is 1. i.e. linear equations has no exponents on their variables. The graph of a linear equation is a straight line. To graph a linear equation, we identify two values (x-valu
From playlist ⚡️Graph Linear Equations | Learn About
Intro to Linear Systems: 2 Equations, 2 Unknowns - Dr Chris Tisdell Live Stream
Free ebook http://tinyurl.com/EngMathYT Basic introduction to linear systems. We discuss the case with 2 equations and 2 unknowns. A linear system is a mathematical model of a system based on the use of a linear operator. Linear systems typically exhibit features and properties that ar
From playlist Intro to Linear Systems
Aaron Sidford: Introduction to interior point methods for discrete optimization, lecture I
Over the past decade interior point methods (IPMs) have played a pivotal role in mul- tiple algorithmic advances. IPMs have been leveraged to obtain improved running times for solving a growing list of both continuous and combinatorial optimization problems including maximum flow, bipartit
From playlist Summer School on modern directions in discrete optimization
Rasmus Kyng: Two-Commodity Flow is as Hard as Linear Programming
We give a nearly-linear time reduction that encodes any linear program polynomially bounded coefficients and solution as a 2-commodityflow problem with only a polylogarithmic blow-up in size. Our reduction applies to high-accuracy approximation algorithms and exact algorithms. Our reductio
From playlist Workshop: Approximation and Relaxation
Proving super-polynomial lower bounds for syntactic multilinear branching programs by Ramya C
Discussion Meeting Workshop on Algebraic Complexity Theory  ORGANIZERS Prahladh Harsha, Ramprasad Saptharishi and Srikanth Srinivasan DATE & TIME 25 March 2019 to 29 March 2019 VENUE Madhava Lecture Hall, ICTS Bangalore Algebraic complexity aims at understanding the computationa
From playlist Workshop on Algebraic Complexity Theory 2019
Proofs & Goofs Ep1: Linear Programming #SoME2
Hey everybody! My name's Max Fishelson. I'm a CS theory PhD student at MIT. I like teaching math and singing songs. I hope you enjoy! maxkfish.com
From playlist Summer of Math Exposition 2 videos
Nonlinear algebra, Lecture 11: "Semidefinite Programming", by Bernd Sturmfels
This is the eleventh lecture in the IMPRS Ringvorlesung, the advanced graduate course at the Max Planck Institute for Mathematics in the Sciences.
From playlist IMPRS Ringvorlesung - Introduction to Nonlinear Algebra
Approximating Max Cut with Subexponential Linear Programs - Tselil Schramm
Computer Science/Discrete Mathematics Seminar I Topic: Approximating Max Cut with Subexponential Linear Programs Speaker: Tselil Schramm Affiliation: Stanford University Date: March 29, 2021 For more video please visit http://video.ias.edu
From playlist Mathematics
M. Grazia Speranza: "Fundamentals of optimization" (Part 1/2)
Watch part 2/2 here: https://youtu.be/ZJA4B2IePis Mathematical Challenges and Opportunities for Autonomous Vehicles Tutorials 2020 "Fundamentals of optimization" (Part 1/2) M. Grazia Speranza - University of Brescia Institute for Pure and Applied Mathematics, UCLA September 22, 2020 Fo
From playlist Mathematical Challenges and Opportunities for Autonomous Vehicles 2020
This is part of an online course on beginner/intermediate linear algebra, which presents theory and implementation in MATLAB and Python. The course is designed for people interested in applying linear algebra to applications in multivariate signal processing, statistics, and data science.
From playlist Linear algebra: theory and implementation
Elias Khalil - Neur2SP: Neural Two-Stage Stochastic Programming - IPAM at UCLA
Recorded 02 March 2023. Elias Khalil of the University of Toronto presents "Neur2SP: Neural Two-Stage Stochastic Programming" at IPAM's Artificial Intelligence and Discrete Optimization Workshop. Abstract: Stochastic Programming is a powerful modeling framework for decision-making under un
From playlist 2023 Artificial Intelligence and Discrete Optimization
Linear Programming - Explanation and Example
This video is about Linear Programming - Explanation and Example
From playlist Optimization
What is the slope of a linear equation
👉 Learn about graphing linear equations. A linear equation is an equation whose highest exponent on its variable(s) is 1. i.e. linear equations has no exponents on their variables. The graph of a linear equation is a straight line. To graph a linear equation, we identify two values (x-valu
From playlist ⚡️Graph Linear Equations | Learn About
24. Linear Programming and Two-Person Games
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 This lecture focus
From playlist MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018