CS 269 : Machine Learning Theory Lecture 16 : SVMs and Kernels
نویسندگان
چکیده
We previously showed that the solution to the primal problem is equivalent to the solution to the dual problem if they satisfy the following primal-dual equivalence conditions. First, we need a convex objective function and in our case, it is 1 2 ||~ w||2. Second, we need convex inequality constraints gi, which are 1−yi(~ w · ~xi + b) for i = 1, ...,m. The last condition states that for each inequality gi, there exists some value of the variables that make gi strictly less than 0. Since these conditions are satisfied for the optimization problem we defined, we know that we can solve the dual version of the problem instead of the primal problem and the solutions will be equivalent.
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