Exact line search and backtracking line search

Assume we are trying to minimize some convex function which is differentiable. One way to do this is to use a descent method. A general descent method can be described as follows: Given a starting point in the domain of , iterate over the following 3 steps until some stopping criterion is satisfied: Choose a […]

Exact line search and backtracking line search

The Lagrange dual function is always concave

Consider an optimization problem in standard form: with the variable . Let be the domain for , i.e. the intersection of the domains of the ‘s and the ‘s. The Lagrangian associated with this problem is the function defined as with domain . The Lagrange dual function is the function defined as the minimum value […]

The Lagrange dual function is always concave