In the the optimization problem with slack variables for support vector machine, C is used as a balancing coefficient between the square norm of w and the sum of slack variables. See this link for C https://stackoverflow.com/questions/35848210/support-vector-machine-what-are-c-gamma.
Assume that we solve the optimization problem with C being one specific value, say C1. Now we change value of C from C1 to C2. I do not want to solve the optimization problem from scratch. Is there any method to modify the solution to get a solution for the case C=C2? Thanks.
Bo Li
The C parameter instructs the SVM optimizer how much you wish to avoid misclassifying each training example. For large values of C, the optimization will select a smaller-margin hyperplane if it performs a better job of accurately classifying all of the training points.
The decision boundary's response to the soft-margin constant, C. A lower C value (right) allows you to disregard points near to the boundary, increasing the margin. A thick line represents the decision border between negative instances (circles) and positive examples (crosses).
Higher C values result in overfitting, which results in a low bias and a high variance. As C approaches positive infinity, there is no tolerance for mistake since the penalty for misclassification is tremendous, resulting in substantial overfitting as the model strives for maximum accuracy.
A nice discussion on this fundamental problem is here : https://www.quora.com/How-can-I-choose-the-parameter-C-for-SVM
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