# Solution to the SVM problem

in support vector machines the idea is to find a decision boundary in which the margin is maximized. This can be written as $$\text{minimize} \ \lVert w \rVert$$ $$\text{subject to} \ \ y_{i}(\boldsymbol{x}_i \cdot \boldsymbol{w}+b) \geq 1$$

What is the optimal decision boundary based on the above minimization problem. I know that this is a quadratic programming problem and various techniques can be used to solve it. But how would you formulate the optimal decision boundary using the above variables?

• Please explain what you mean by "actual" solution. – whuber Jul 18 '14 at 17:19
• @whuber: What is the optimal decision boundary based on the above minimization problem? – svmguy Jul 18 '14 at 17:28
• Why don't you search our site for svm? This question has been explicitly answered--with working code and illustrations--in several threads. – whuber Jul 18 '14 at 17:30