Optimization algorithms and methods

Column generation

Column generation or delayed column generation is an efficient algorithm for solving large linear programs. The overarching idea is that many linear programs are too large to consider all the variables explicitly. The idea is thus to start by solving the considered program with only a subset of its variables. Then iteratively, variables that have the potential to improve the objective function are added to the program. Once it is possible to demonstrate that adding new variables would no longer improve the value of the objective function, the procedure stops. The hope when applying a column generation algorithm is that only a very small fraction of the variables will be generated. This hope is supported by the fact that in the optimal solution, most variables will be non-basic and assume a value of zero, so the optimal solution can be found without them. In many cases, this method allows to solve large linear programs that would otherwise be intractable. The classical example of a problem where it is successfully used is the cutting stock problem. One particular technique in linear programming which uses this kind of approach is the Dantzig–Wolfe decomposition algorithm. Additionally, column generation has been applied to many problems such as crew scheduling, vehicle routing, and the . (Wikipedia).

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Column space of a matrix

We have already looked at the column view of a matrix. In this video lecture I want to expand on this topic to show you that each matrix has a column space. If a matrix is part of a linear system then a linear combination of the columns creates a column space. The vector created by the

From playlist Introducing linear algebra

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In this tutorial I put emphasis of the column view of a matrix of coefficients. We are used to the row view when it comes to systems of linear equations, but it is the column view that is much more fascinating. The column view helps us view a system of linear equations as vectors in a sp

From playlist Introducing linear algebra

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Matrix addition

How do we add matrices. A matrix is an abstract object that exists in its own right, and in this sense, it is similar to a natural number, or a complex number, or even a polynomial. Each element in a matrix has an address by way of the row in which it is and the column in which it is. Y

From playlist Introducing linear algebra

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8 Row and Column Views of a Matrix

The row and column view of a system of linear equations, as well as the matrix as a mathematical object.

From playlist Linear Algebra

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What is a vector? We gently introduce the i and j basis vectors and the idea of a column vector is presented. The algebra of addition, subtraction and scalar multiplication is discussed. Free ebook Free ebook https://bookboon.com/en/introduction-to-vectors-ebook (updated link) Take a sh

From playlist Introduction to Vectors

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Explains the concept of row-echelon from, the form a matrix is in when Gauss elimination is applied to it.

From playlist Linear Algebra

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C69 Introduction to power series

A quick look at power series. They can be used as solutions to linear differential equations with variable coefficients.

From playlist Differential Equations

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Column Vectors - GCSE 9-1 Maths

Here, we look at column vectors! Column vectors are made up of an X vector (the top number) and a y vector (the bottom). We go over what column vectors mean, as well as basic arithmetic: addition, subtraction and multiplication by a scalar! For higher and foundation GCSE 9-1 maths!

From playlist Paper 3 Revision

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Matrices: Leading Rows and leading Columns

What are leading rows and columns in a matrix? What are leading entries?

From playlist Intro to Linear Systems

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From playlist Minitab Tutorial For Beginners

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Jacek Gondzio: Applying interior point algorithms in column generation and cuttingplane methods

Advantages of interior point methods (IPMs) applied in the context of nondifferentiable optimization arising in cutting planes/column generation applications will be discussed. Some of the many false views of the combinatorial optimization community on interior point methods applied in thi

From playlist Workshop: Continuous approaches to discrete optimization

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Xiaoye Sherry Li's (from Lawrence Berkeley National Laboratory) lecture number three on Factorization-based sparse solves and preconditioners

From playlist Gene Golub SIAM Summer School Videos

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Highline Excel 2013 Class Video 38: Excel Text To Columns To Split or Convert Data 7 Examples

Download workbook: http://people.highline.edu/mgirvin/AllClasses/214_2013/214/Busn214_2013.htm This is the Highline Community College Class, Spreadsheet Construction taught by Michael Girvin: Basic To Advanced Excel. Topics in this video: 1. Split Text with Delimiter = Space. Split First a

From playlist Highline Complete Excel 2013 Class: Comprehensive Excel (Basics To Advanced)

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SQL Tutorial For Beginners 2022 | SQL Q&A | SQL Training And Certification | Simplilearn

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From playlist Simplilearn Live

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Part 11 - WordPress Theme Development - Manage and Create Custom Columns

:: Support Me :: http://www.alecaddd.com/support-me/ How to build a Premium Theme for WordPress - Lesson 11 Manage and Create Custom Columns GitHub Repo: https://github.com/Alecaddd/Sunset-theme Download Sunset Theme FREE: https://www.youtube.com/watch?v=ViZLtFIcSfo :: Tutorial Series

From playlist Create a Premium WordPress Theme

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5. Error correction, syndrome decoding

MIT 6.02 Introduction to EECS II: Digital Communication Systems, Fall 2012 View the complete course: http://ocw.mit.edu/6-02F12 Instructor: George Verghese This lecture continues to explore error correction through a closer look at the generator matrix and the parity check matrix. Syndrom

From playlist MIT 6.02 Introduction to EECS II: Digital Communication Systems, Fall 2012

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Math 060 090617 Lecture #03 Matrix multiplication and systems of linear equations

Review of conventions of the text; *matrix multiplication*; "key observation" about multiplication (left multiplication occurs column-wise); relation with systems of linear equations. Rephrasals of what it means to find a solution (in terms of linear combinations, span). #matrixmultiplic

From playlist Course 4: Linear Algebra (Fall 2017)

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Hibernate Tutorial 11 - Configuring Collections and Adding Keys

More configuration options for collections, including configuring primary keys.

From playlist Hibernate

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Combining Logs 2

This is an worked example of logarithms in Algebra 2.

From playlist Logs Group Quiz

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Linear Algebra 1.3 Matrices and Matrix Operations

My notes are available at http://asherbroberts.com/ (so you can write along with me). Elementary Linear Algebra: Applications Version 12th Edition by Howard Anton, Chris Rorres, and Anton Kaul

From playlist Linear Algebra

Related pages

Reduced cost | Crew scheduling | Dantzig–Wolfe decomposition | Cutting stock problem | Dual linear program | Without loss of generality | Linear programming