Article directory
1. Mathematical optimization
Mathematical optimization is the process of finding the best set of inputs that maximize (or minimize) the output of a function. In the field of optimization, the function to be optimized is called the objective function. A large number of out-of-the-box tools exist for solving optimization problems, although these only work with well-behaved functions, also known as convex functions. A well-behaved function contains an optimal value, either a maximum or a minimum. Here we can think of the function as a surface with a single valley (min) and/or hill (max). So a non-convex function is like a surface with multiple valleys and hills.
Optimization of convex functions, also known as convex optimization, is suitable for simple tasks such as portfolio optimization, flight scheduling, developing optimal advertisements, and machine learning. In the context of machine learning, convex optimization comes into play when training several machine learning models, including linear regression, logistic regression, and support vector machines.
One limitation of convex optimization is that it assumes that the objective function is guaranteed to have a valley and/or hill