Why might it be sometimes easier to solve the dual problem rather than the primal one?

Sometimes the dual is easier to solve. Thus the fewer the constraints, the smaller the size of the basis matrix, and thus the fewer computations required in each iteration of the simplex method.

What is the advantage of the dual formulation of SVM?

The main advantage of dual form of SVM over lagrange formulation is that it only depends on the ∝. The formulation uptill now what we have seen are all called Hard Margin SVM. This works well when the data is linearly separable. But the biggest issue with this is that the real world data is often noisy.

What is the difference between primal and dual?

In the primal problem, the objective function is a linear combination of n variables. In the dual problem, the objective function is a linear combination of the m values that are the limits in the m constraints from the primal problem.

Why is dual problem always convex?

Although the primal problem is not required to be convex, the dual problem is always convex. maximization problem, which is a convex optimization problem. The Lagrangian dual problem yields a lower bound for the primal problem. It always holds true that f⋆ ≥ g⋆, called as weak duality.

Why do we need dual problems in SVM?

In mathematical optimization theory, duality means that optimization problems may be viewed from either of two perspectives, the primal problem or the dual problem (the duality principle). The solution to the dual problem provides a lower bound to the solution of the primal (minimization) problem.

Do primal and dual have the same optimal solution?

As the simplex method progresses, the solutions determined for the dual problem are all infeasible until the optimal solution is attained for the primal problem. The dual solution corresponding to the optimal primal solution is both optimal and feasible.

What is the difference between primal and dual in linear programming?

Explanation: The solution to the dual problem provides a lower bound to the solution of the primal (minimization) problem. However in general the optimal values of the primal and dual problems need not be equal. Their difference is called the duality gap.

Why is the dual always concave?

The dual function is concave even when the optimization problem is not convex, since the dual function is the pointwise infimum of a family of affine functions of (λ, ν) (a different affine function for each x ∈ D).