Let the problem is min f(x1, x2, …, xn) subject to h1(x1, x2, …, xn) = 0. And it converted it into min L(x1, x2, …, xn, λ) = min {f(x1, x2, …, xn) – λh1 (x1, x2, …, xn)}. Then L(x, λ), λ are known as Lagrangian function and Lagrangian function respectively.

Quiz on support vector machines (SVMs), covering key concepts like the large margin intuition, margins and hard/soft SVMs, norm regularization, optimality conditions and support vectors, and finally, implementing soft SVMs using Stochastic Gradient Descent (SGD). A support vector machine (SVM) is a supervised machine learning algorithm that can generalize between two classes. SVMs are used for classification and regression tasks, and are particularly good at solving binary classification problems.  Here are some details about SVMs: Objective: Find a hyperplane with the highest margin,... Show more

Quiz on support vector machines (SVMs), covering key concepts like the large margin intuition, margins and hard/soft SVMs, norm regularization, optimality conditions and support vectors, and finally, implementing soft SVMs using Stochastic Gradient Descent (SGD).

A support vector machine (SVM) is a supervised machine learning algorithm that can generalize between two classes. SVMs are used for classification and regression tasks, and are particularly good at solving binary classification problems. 

Here are some details about SVMs:

Objective: Find a hyperplane with the highest margin, which is the maximum distance between the two classes. This makes it easier to classify new data points in the future.
Data points: For linearly separable data, SVM takes all data points into consideration. For linearly non-separable data, SVM uses kernel tricks to make the data linearly separable.
Kernels: SVM kernels are functions based on which we can transform the data so that it is easier to fit a hyperplane to segregate the points better.
Support vectors: The closest data points, known as support vectors, lie on the margins and determine the position of the hyperplane.

Advantages
SVMs perform well at classifying non-linear data. They also optimize margins to help reduce the overfitting of data and allow for capacity control. 
SVMs can be used for a variety of tasks, such as: text classification, image classification, spam detection, and handwriting identification.

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