Mathematical optimization (alternatively spelled optimisation) or mathematical programming is the selection of a best element, with regard to some criteria, from some set of available alternatives. [1][2] It is generally divided into two subfields: discrete optimization and continuous optimization.
Optimization, collection of mathematical principles and methods used for solving quantitative problems. Optimization problems typically have three fundamental elements: a quantity to be maximized or minimized, a collection of variables, and a set of constraints that restrict the variables.
Optimization is the process of finding the best possible solution from a set of available options, based on some measure of what “best” means. In mathematical terms, it means adjusting a set of variables to either maximize or minimize a target value, often while respecting certain limits.
The meaning of OPTIMIZATION is an act, process, or methodology of making something (such as a design, system, or decision) as fully perfect, functional, or effective as possible; specifically : the mathematical procedures (such as finding the maximum of a function) involved in this.
In optimization problems we are looking for the largest value or the smallest value that a function can take. We saw how to solve one kind of optimization problem in the Absolute Extrema section where we found the largest and smallest value that a function would take on an interval.
Why optimization? In some sense, all engineering design is optimization: choosing design parameters to improve some objective Much of data analysis is also optimization: extracting some model parameters from data while minimizing some error measure (e.g. fitting)
Optimization problem: Maximizing or minimizing some function relative to some set, often representing a range of choices available in a certain situation. The function allows comparison of the different choices for determining which might be “best.”