Linear programmingLinear programming (LP), also called linear optimization, is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements and objective are represented by linear relationships. Linear programming is a special case of mathematical programming (also known as mathematical optimization). More formally, linear programming is a technique for the optimization of a linearobjective function, subject to linear equality and linear inequalityconstraints. Its feasibl...
Convex functionIn mathematics, a real-valued function is called convex if the line segment between any two distinct points on the graph of the function lies above or on the graph of the function between the two points. Equivalently, a function is convex if its epigraph (the set of points on or above the graph of the function) is a convex set. In simple terms, a convex function graph is shaped like a cup ∪{\displaystyle \cup } (or a straight line like a linear function), while a concave function's graph is shaped like a cap �...
Optimization problemIn mathematics, engineering, computer science and economics, an optimization problem is the problem of finding the best solution from all feasible solutions. Optimization problems can be divided into two categories, depending on whether the variables are continuous or discrete: An optimization problem with discrete variables is known as a discrete optimization, in which an object such as an integer, permutation or graph must be found from a countable set. A problem with continuous variables is known as a continu...
Continuous optimizationContinuous optimization is a branch of optimization in applied mathematics. As opposed to discrete optimization, the variables used in the objective function are required to be continuous variables—that is, to be chosen from a set of real values between which there are no gaps (values from intervals of the real line). Because of this continuity assumption, continuous optimization allows the use of calculus techniques.
Value (mathematics)In mathematics, a mathematical value is a broad term that refers to any definite entity that can be manipulated with operators according to the well-defined rules of its mathematical system. Certain values can correspond to the real world, although most values in mathematics generally exists purely as abstract objects with no connection to the real world. Numerical valuesNumbers (specifically the reals) are values that represent quantities. In that sense, numerical values are values that comprises or are made up...
Maximum and minimumIn mathematical analysis, the maximum and minimum of a function are, respectively, the greatest and least value taken by the function. Known generically as extrema, they may be defined either within a given range (the local or relative extrema) or on the entire domain (the global or absolute extrema) of a function. Pierre de Fermat was one of the first mathematicians to propose a general technique, adequality, for finding the maxima and minima of functions. As defined in set theory, the maximum and minimum of a ...
Argument of a functionIn mathematics, an argument of a function is a value provided to obtain the function's result. It is also called an independent variable. For example, the binary function f ( x , y ) = x 2 + y 2 {\displaystyle f(x,y)=x^{2}+y^{2}} has two arguments, x {\displaystyle x} and y {\displaystyle y} , in an ordered pair ( x , y ) {\displaystyle (x,y)} . The hypergeometric function is an example of a four-argument function. The number of arguments that a function takes is called the arity of the function. A function that...
Function of a real variableIn mathematics, a function of a real variable is a function whose domain is a subset of R{\displaystyle \mathbb {R} }. Many real functions that are often encountered have their domain contain an interval of non-empty interior, and may be continuous, or have some degree of smoothness, over one or more intervals, each of non-empty interior, in the domain. In older texts, the theory of functions of a real variable is often synonymous with what is usually now called real analysis. The most widely considered such fun...
MathematicsMathematics is a field of knowledge concerned with abstract concepts such as numbers, geometric shapes, sets, functions, and probabilities. It uses logical reasoning and proof to study and establish their properties, often expressed as theorems, formulas, and equations. Mathematics is used to model and solve problems in science, engineering, technology, economics, and everyday life. There are many areas of mathematics, including number theory (the study of integers and their properties), algebra (the study of op...
Applied mathematicsApplied mathematics is the application of mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, social science, and industry. Thus, applied mathematics is a combination of mathematical science and specialized knowledge. The term "applied mathematics" also describes the professional specialty in which mathematicians work on practical problems by formulating and studying mathematical models. In the past, practical applications have motivated ...
Computer scienceComputer science is the study of computation, information, and automation. Included broadly in the sciences, computer science spans theoretical disciplines (such as algorithms, theory of computation, and information theory) to applied disciplines (including the design and implementation of hardware and software). An expert in the field is known as a computer scientist. Algorithms and data structures are central to computer science. The theory of computation concerns abstract models of computation and general cla...
EngineeringEngineering is the practice of systematically applying natural science and mathematics to design and improve systems, devices, or processes that solve problems under constraints. It is typically motivated by satisfying human needs, resulting in creations such as bridges, engines, smartphones, pacemakers, the internet, spacecraft, and washing machines. Engineering involves balancing competing demands such as safety, performance, aesthetics, cost, laws and regulations, and time, while operating within fundamental ...
EconomicsEconomics () is a social science that studies the production, distribution, and consumption of goods and services. Economics focuses on the behaviour and interactions of economic agents and how economies work. Microeconomics analyses what is viewed as the basic elements of economies, including individual agents and markets, their interactions, and the outcomes of those interactions. Individual agents may include households, firms, buyers, and sellers. Macroeconomics analyses economies as systems where production...*As an Amazon Associate I earn from qualifying purchases.