In this post we'll discuss constrained optimization. We'll also see some some techniques to solve such problems, the Predictor-Corrector (PC) Algorithm , the most widely used Algorithm and sits behind many solvers. Idea here is to implement the PC algorithm for Quadratic Optimization problem and then use it to solve Support Vector Machine problem.
Constrained Optimization
The general form of any constrained optimization problem can be written as:
\begin{array}{ll} \text{maximize} & c^T x \\ \text{subject to}& A^T x = b \\ &0 \le x \le 1. \end{array}