The dual of a given linear program (LP) is another LP that is derived from the original (the primal) LP in the following schematic way: * Each variable in the primal LP becomes a constraint in the dual LP; * Each constraint in the primal LP becomes a variable in the dual LP; * The objective direction is inversed – maximum in the primal becomes minimum in the dual and vice versa. The weak duality theorem states that the objective value of the dual LP at any feasible solution is always a bound on the objective of the primal LP at any feasible solution (upper or lower bound, depending on whether it is a maximization or minimization problem). In fact, this bounding property holds for the optimal values of the dual and primal LPs. The strong duality theorem states that, moreover, if the primal has an optimal solution then the dual has an optimal solution too, and the two optima are equal. These theorems belong to a larger class of duality theorems in optimization. The strong duality theorem is one of the cases in which the duality gap (the gap between the optimum of the primal and the optimum of the dual) is 0. (Wikipedia).
Solving an equation with multiple decimals
👉 Learn how to solve two step linear equations. A linear equation is an equation whose highest exponent on its variable(s) is 1. To solve for a variable in a two step linear equation, we first isolate the variable by using inverse operations (addition or subtraction) to move like terms to
From playlist How to Solve One Step Equations with Decimals
Solve for the zeros of a linear equation
👉 Learn how to solve two step linear equations. A linear equation is an equation whose highest exponent on its variable(s) is 1. To solve for a variable in a two step linear equation, we first isolate the variable by using inverse operations (addition or subtraction) to move like terms to
From playlist Solve Two Step Equations
Solving an equation with variable on the same side
👉 Learn how to solve two step linear equations. A linear equation is an equation whose highest exponent on its variable(s) is 1. To solve for a variable in a two step linear equation, we first isolate the variable by using inverse operations (addition or subtraction) to move like terms to
From playlist Solve Two Step Equations with Two Variables
Learning to solve a two step equation with inverse operations 2y+5=19
👉 Learn how to solve two step linear equations. A linear equation is an equation whose highest exponent on its variable(s) is 1. To solve for a variable in a two step linear equation, we first isolate the variable by using inverse operations (addition or subtraction) to move like terms to
From playlist Solve Two Step Equations
Solving an equation by combining like terms
👉 Learn how to solve two step linear equations. A linear equation is an equation whose highest exponent on its variable(s) is 1. To solve for a variable in a two step linear equation, we first isolate the variable by using inverse operations (addition or subtraction) to move like terms to
From playlist Solve Two Step Equations with Two Variables
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
Gerard Cornuejols: Dyadic linear programming
A finite vector is dyadic if each of its entries is a dyadic rational number, i.e. if it has an exact floating point representation. We study the problem of finding a dyadic optimal solution to a linear program, if one exists. This is joint work with Ahmad Abdi, Bertrand Guenin and Levent
From playlist Workshop: Continuous approaches to discrete optimization
Francisco Criado: The dual 1-fair packing problem and applications to linear programming
Proportional fairness (also known as 1-fairness) is a fairness scheme for the resource allocation problem introduced by Nash in 1950. Under this scheme, an allocation for two players is unfair if a small transfer of resources between two players results in a proportional increase in the ut
From playlist Workshop: Tropical geometry and the geometry of linear programming
Delayed column generation in large scale integer optimization problems - Professor Raphael Hauser
Mixed linear integer programming problems play an important role in many applications of decision mathematics, including data science. Algorithms typically solve such problems via a sequence of linear programming approximations and a divide-and-conquer approach (branch-and-bound, branch-an
From playlist Data science classes
Association schemes and codes I: The Delsarte linear program - Leonardo Coregliano
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From playlist Mathematics
Aaron Sidford: Introduction to interior point methods for discrete optimization, lecture II
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
Lecture 8 | Convex Optimization I (Stanford)
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From playlist Lecture Collection | Convex Optimization
Lec 29 | MIT 18.085 Computational Science and Engineering I
Applications in signal and image processing: compression A more recent version of this course is available at: http://ocw.mit.edu/18-085f08 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 18.085 Computational Science & Engineering I, Fall 2007
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From playlist cs273a
👉 Learn how to solve two step linear equations. A linear equation is an equation whose highest exponent on its variable(s) is 1. To solve for a variable in a two step linear equation, we first isolate the variable by using inverse operations (addition or subtraction) to move like terms to
From playlist Solve Two Step Equations
👉 Learn how to solve two step linear equations. A linear equation is an equation whose highest exponent on its variable(s) is 1. To solve for a variable in a two step linear equation, we first isolate the variable by using inverse operations (addition or subtraction) to move like terms to
From playlist Solve Two Step Equations
👉 Learn how to solve two step linear equations. A linear equation is an equation whose highest exponent on its variable(s) is 1. To solve for a variable in a two step linear equation, we first isolate the variable by using inverse operations (addition or subtraction) to move like terms to
From playlist Solve Two Step Equations
Decision Making and Inference Under Model Misspecification by Jose Blanchet
PROGRAM: ADVANCES IN APPLIED PROBABILITY ORGANIZERS: Vivek Borkar, Sandeep Juneja, Kavita Ramanan, Devavrat Shah, and Piyush Srivastava DATE & TIME: 05 August 2019 to 17 August 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Applied probability has seen a revolutionary growth in resear
From playlist Advances in Applied Probability 2019
👉 Learn how to solve two step linear equations. A linear equation is an equation whose highest exponent on its variable(s) is 1. To solve for a variable in a two step linear equation, we first isolate the variable by using inverse operations (addition or subtraction) to move like terms to
From playlist Solve Two Step Equations
👉 Learn how to solve two step linear equations. A linear equation is an equation whose highest exponent on its variable(s) is 1. To solve for a variable in a two step linear equation, we first isolate the variable by using inverse operations (addition or subtraction) to move like terms to
From playlist Solve Two Step Equations