Objective function, Linearity and nonlinearity

This lecture delves into the concepts of linear and non-linear functions in optimization. It explains how linear functions can be simplified by expressing them as linear combinations of variables, while non-linear functions present varying levels of difficulty. The lecture also introduces the concept of affine functions, which are linear functions shifted by a constant. It discusses how adding a constant to an objective function in optimization does not impact the outcome. The instructor illustrates the difference between linear and non-linear functions using graphical representations and explains how Lipschitz continuity of the gradient can be used to measure the level of non-linearity in a function. By the end of the lecture, viewers will have a clear understanding of the distinctions between linear and non-linear functions in optimization.