# lagrange multipliers

Published articles for lagrange multipliers.

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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.

## A Reminder of Lagrange Multipliers for Optimization Problems

DevFeed: [A Reminder of Lagrange Multipliers for Optimization Problems](<https://devfeed.tech/articles/lagrangians-for-the-amnesiac-40334.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2013/11/30/lagrangians-for-the-amnesiac/>)

Published: 2013-11-30T09:00:50Z

Content type: tutorial

Language: en

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

Topics: [Optimization](<https://devfeed.tech/topics/optimization.md>), [function](<https://devfeed.tech/topics/function.md>), [Variable](<https://devfeed.tech/topics/variable.md>)

Tags: [convex-functions](<https://devfeed.tech/tags/convex-functions.md>), [function](<https://devfeed.tech/tags/function.md>), [gradient-descent](<https://devfeed.tech/tags/gradient-descent.md>), [lagrange](<https://devfeed.tech/tags/lagrange.md>), [lagrange-multipliers](<https://devfeed.tech/tags/lagrange-multipliers.md>), [linear-algebra](<https://devfeed.tech/tags/linear-algebra.md>), [optimization](<https://devfeed.tech/tags/optimization.md>), [problems](<https://devfeed.tech/tags/problems.md>), [variable](<https://devfeed.tech/tags/variable.md>), [vectors](<https://devfeed.tech/tags/vectors.md>)

### AI overview

A tutorial-style reminder of Lagrange multipliers for optimization problems. It reviews gradients, partial derivatives, dot products, and directional change for multivariable functions.

### Source excerpt

For a while I've been meaning to do some more advanced posts on optimization problems of all flavors. One technique that comes up over and over again is Lagrange multipliers, so this post is going to be a leisurely reminder of that technique. I often forget how to do these basic calculus-type things, so it's good practice. We will assume something about the reader's knowledge, but it's a short list: know how to operate with vectors and the dot product, know how to take a partial derivative, and know that in single-variable calculus the local maxima and minima of a differentiable function $ f(x)$ occur when the derivative $ f'(x)$ vanishes.