Consider the picture attached the algorithm of coordinate descent of the Coordinate Descent Algorithm taken from Wright, Stephen J., Coordinate descent algorithms, Math. Program. 151, No. 1 (B), 3-34 (2015). ZBL1317.49038.
Its explanation says ".... Turning to step-length αlpha-k, we may perform exact minimization along the ik component, or choose a value of αlpha-k that satisfies traditional line-search conditions (such as sufficient decrease), or make a predefined “short-step” choice of αlpha-k based on prior knowledge of the properties of f." I want to ask the following: 1. the explanation which says that we may perform exact minimization along the ik component, what does it mean? 2. Can I have some examples or relevant material which shows this concept through an example. Thank you in advance
