Mathematical and Numerical Optimization

An optimization problem consists of three basic components, which are, an objective function, a set of unknown variables, and a set of constraints. The area of mathematical and numerical optimization is devoted to the study of both theoretical properties and practical solution techniques for optimization problems of various forms. Optimization problems with multiple objectives are typically reformulated as single objective problems and then transformed into a standard optimization problem. Optimization problems are categorized according to the form of the objective function and the functions defining the constraints. Some examples of common optimization problems are linear programming, quadratic programming, convex programming, and nonlinear programming. Of all the optimization problems Linear programming (LP) is the best known and the most frequently solved optimization problem in the real world.