Mathematical optimization

In mathematics, computer science and operations research, mathematical optimization (alternatively, optimization or mathematical programming) is the selection of a best element (with regard to some criteria) from some set of available alternatives.

In the simplest case, an optimization problem consists of maximizing or minimizing a real function by systematically choosing input values from within an allowed set and computing the value of the function. The generalization of optimization theory and techniques to other formulations comprises a large area of applied mathematics. More generally, optimization includes finding "best available" values of some objective function given a defined domain (or a set of constraints), including a variety of different types of objective functions and different types of domains.

Optimization problems

An optimization problem can be represented in the following way:

Such a formulation is called an optimization problem or a mathematical programming problem (a term not directly related to computer programming, but still in use for example in linear programming – see History below). Many real-world and theoretical problems may be modeled in this general framework. Problems formulated using this technique in the fields of physics and computer vision may refer to the technique as energy minimization, speaking of the value of the function f as representing the energy of the system being modeled.

Optimization (role-playing games)

Optimisation, in computer and table-top role-playing games, is a term intended to describe a play style or set of play styles alternately referred to by the terms munchkin gaming, powergaming, min-maxing, "roll-playing", or twinking, but without the pejorative connotation of those terms. The core idea of optimization as a play style is that of deriving enjoyment from choosing and benefiting from the game mechanical options that best optimize one's character's performance for some specific purpose—most commonly, speed of power or wealth accumulation. Players who primarily enjoy this play style are called optimizers. This reflects, at least in large part, an effort by game developers and operators to recognize and validate this style of play, and to be able to discuss it and the players who enjoy it without resorting to the traditional, pejorative terms.

Infrastructure optimization

Infrastructure optimization is Microsoft's structured, systematic process for assessing an organization's IT infrastructure and application platform across capabilities in order to provide an optimization roadmap toward a Dynamic IT. The roadmap helps companies to define and implement optimization initiatives that will enable proactive, IT management and deliver cost and risk reductions across the IT organization. These optimization initiatives also enhance user needs and user experience in order to increase productivity and amplify the impact of employees. Optimization enables a business to realize the full value of its IT infrastructure and platform investments and establishes IT as a strategic business asset that can facilitate innovation and help organizations respond quickly to change.

In order to help customers assess the effectiveness and potential of their IT infrastructure and application platform, create agility, and reduce costs, Microsoft has developed three Optimization models based on industry and analyst work. The Optimization models are vendor agnostic, "All of the up-front questions are about general technologies, not specific products." Optimization can be viewed in three perspectives: