What is a primal maximization problem?
In the primal problem, the objective function is a linear combination of n variables. The goal is to maximize the value of the objective function subject to the constraints. A solution is a vector (a list) of n values that achieves the maximum value for the objective function.
What is symmetric primal dual problem?
There are three types of Primal- Dual problems. 1. Symmetric: Here all constraints of both primal and dual problems are in equations and variables are non negative. Mixed type: Here some constraints of primal are equations and some variables are unrestricted in sign.
Why bother with the dual problem when fitting SVM?
3. The dual problem can now be solved efficiently, i.e. via a dual coordinate descent algorithm that yields an epsilon-optimal solution in O ( log ( 1 ε)). This is done by noting that fixing all alphas except one yields a closed-form solution.
How is the primal and dual optimization problem differentiable?
This optimization problem is differentiable and convex •the KKT conditions and necessary and sufficient conditions for primal/dual optimality (with zero duality gap) •we can use these conditions to find a relationship between the solutions of the primal and dual problems •the dual optimization problem will be easy to “kernelize”
Which is the best definition of primal duality?
Primal: Dual: Weak duality: Strong duality: For convex problems with affine constraints Saddle point property If are primal/dual optimal with zero duality gap, they are a saddle pointof , i.e., for all , ,
Is the dual problem a non convex problem?
In my opinion in the lecture notes of Andrew ng, its been clearly mentioned that the primal problem of 1/||w||, is a non convex problem. The dual is a convex problem and its always easy to find the optimum of a convex function.