# simplex algorithm

Published articles for simplex algorithm.

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## Duality for the SVM

DevFeed: [Duality for the SVM](<https://devfeed.tech/articles/duality-for-the-svm-40412.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2017/06/12/duality-for-the-svm/>)

Published: 2017-06-12T08:00:50Z

Content type: tutorial

Language: en

Sources: [Jeremy Kun](<https://devfeed.tech/sources/jeremy-kun.md>)

Topics: [Optimization](<https://devfeed.tech/topics/optimization.md>), [Programming](<https://devfeed.tech/topics/programming.md>), [Algorithm](<https://devfeed.tech/topics/algorithm.md>)

Tags: [algorithm](<https://devfeed.tech/tags/algorithm.md>), [lagrange-multipliers](<https://devfeed.tech/tags/lagrange-multipliers.md>), [linear-programming](<https://devfeed.tech/tags/linear-programming.md>), [optimization](<https://devfeed.tech/tags/optimization.md>), [programming](<https://devfeed.tech/tags/programming.md>), [simplex-algorithm](<https://devfeed.tech/tags/simplex-algorithm.md>)

### AI overview

This tutorial explains how the Karush-Kuhn-Tucker theorem applies to the support vector machine optimization problem. It introduces the structure of convex quadratic optimization and states the conditions involving gradients, primal and dual constraints, and complementary slackness.

### Source excerpt

This post is a sequel to Formulating the Support Vector Machine Optimization Problem. The Karush-Kuhn-Tucker theorem Generic optimization problems are hard to solve efficiently. However, optimization problems whose objective and constraints have special structure often succumb to analytic simplifications. For example, if you want to optimize a linear function subject to linear equality constraints, one can compute the Lagrangian of the system and find the zeros of its gradient. More generally, optimizing a linear function subject to linear equality and inequality constraints can be solved using various so-called "linear programming" techniques, such as the simplex algorithm.

## Linear Programming and the Simplex Algorithm

DevFeed: [Linear Programming and the Simplex Algorithm](<https://devfeed.tech/articles/linear-programming-and-the-simplex-algorithm-40371.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2014/12/01/linear-programming-and-the-simplex-algorithm/>)

Published: 2014-12-01T10:00:59Z

Content type: tutorial

Language: en

Sources: [Jeremy Kun](<https://devfeed.tech/sources/jeremy-kun.md>)

Topics: [Algorithm](<https://devfeed.tech/topics/algorithm.md>), [Programming](<https://devfeed.tech/topics/programming.md>)

Tags: [algorithm](<https://devfeed.tech/tags/algorithm.md>), [code](<https://devfeed.tech/tags/code.md>), [exponential-time-algorithms](<https://devfeed.tech/tags/exponential-time-algorithms.md>), [integer-programming](<https://devfeed.tech/tags/integer-programming.md>), [linear-algebra](<https://devfeed.tech/tags/linear-algebra.md>), [linear-programming](<https://devfeed.tech/tags/linear-programming.md>), [lp-relaxation](<https://devfeed.tech/tags/lp-relaxation.md>), [optimization](<https://devfeed.tech/tags/optimization.md>), [programming](<https://devfeed.tech/tags/programming.md>), [row-reduction](<https://devfeed.tech/tags/row-reduction.md>), [simplex-algorithm](<https://devfeed.tech/tags/simplex-algorithm.md>)

### AI overview

This tutorial explains how to implement the simplex algorithm for solving linear programs. It introduces standard form and shows how slack variables convert inequality constraints into equality constraints.

### Source excerpt

In the last post in this series we saw some simple examples of linear programs, derived the concept of a dual linear program, and saw the duality theorem and the complementary slackness conditions which give a rough sketch of the stopping criterion for an algorithm. This time we'll go ahead and write this algorithm for solving linear programs, and next time we'll apply the algorithm to an industry-strength version of the nutrition problem we saw last time.