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...
SimplexIn geometry, a simplex (plural: simplexes or simplices) is a generalization of the notion of a triangle or tetrahedron to arbitrary dimensions. The simplex is so-named because it represents the simplest possible polytope in any given dimension. For example, a 0-dimensional simplex is a point,a 1-dimensional simplex is a line segment,a 2-dimensional simplex is a triangle,a 3-dimensional simplex is a tetrahedron, anda 4-dimensional simplex is a 5-cell.Specifically, a k-simplex is a k-dimensional polytope that is t...
George DantzigGeorge Bernard Dantzig (; November 8, 1914 – May 13, 2005) was an American mathematical scientist who made contributions to industrial engineering, operations research, computer science, economics, and statistics. Dantzig is known for his development of the simplex algorithm, an algorithm for solving linear programming problems, and for his other work with linear programming. In statistics, Dantzig solved two open problems in statistical theory, which he had mistaken for homework after arriving late to a lectu...
AlgorithmIn mathematics and computer science, an algorithm () is any well-defined set of instructions that when followed terminates after a finite number of steps that comprise a solution to a given computational problem. Advanced algorithms may utilize loops and involve many conditionals that decide the next step based on the inputs provided, resulting in long sequences of steps before halting, but all algorithms terminate by definition. In contrast to algorithms, heuristics might be applied to problems for which it is ...
Lebesgue integralMethod of mathematical integration The integral of a positive function can be interpreted as the area under a curve. Part of a series of articles aboutCalculus ∫ a b f ′ ( t ) d t = f ( b ) − f ( a ) {\displaystyle \int _{a}^{b}f'(t)\,dt=f(b)-f(a)} Fundamental theorem Limits Continuity Rolle's theorem Mean value theorem Inverse function theorem Differential Definitions Derivative (generalizations) Differential infinitesimal of a function total Concepts Differentiation notation Second derivative Implicit di...
Linear inequalityIn mathematics a linear inequality is an inequality which involves a linear function. A linear inequality contains one of the symbols of inequality: < less than> greater than≤ less than or equal to≥ greater than or equal to≠ not equal toA linear inequality looks exactly like a linear equation, with the inequality sign replacing the equality sign. Linear inequalities of real numbersTwo-dimensional linear inequalitiesTwo-dimensional linear inequalities, are expressions in two variables of the form: ax+by<c a...
Jerzy NeymanJerzy Spława-Neyman (pronounced; April 16, 1894 – August 5, 1981) was a Polish mathematician and statistician who first introduced the modern concept of a confidence interval into statistical hypothesis testing and, with Egon Pearson, revised Ronald Fisher's null hypothesis testing. Neyman allocation, an optimal strategy for choosing sample sizes in stratified sampling, is named for him. Spława-Neyman spent the first part of his professional career at various institutions in Warsaw, Poland, and then at Unive...
Wassily LeontiefWassily Wassilyevich Leontief (Russian: Васи́лий Васи́льевич Лео́нтьев; August 5, 1905 – February 5, 1999) was a Russian-American economist known for his research on input–output analysis and how changes in one economic sector may affect other sectors. Leontief was awarded the Nobel Memorial Prize in Economic Sciences in 1973, and four of his doctoral students have also been awarded the prize (Paul Samuelson 1970, Robert Solow 1987, Vernon L. Smith 2002, Thomas Schelling 2005). Bi...
Mechanical calculatorA mechanical calculator, or calculating machine, is a mechanical device used to perform the basic operations of arithmetic automatically, or a simulation like an analog computer or a slide rule. Most mechanical calculators were comparable in size to small desktop computers and have been rendered obsolete by the advent of the electronic calculator and the digital computer. In 1642, Blaise Pascal invented the first operational mechanical calculator with better tens-carry. Concerned about his father's exhausting wo...
PolytopeIn elementary geometry, a polytope is a geometric object with flat sides (faces). Polytopes are the generalization of three-dimensional polyhedra to any number of dimensions. Polytopes may exist in any general number of dimensions n as an n-dimensional polytope or n-polytope. For example, a two-dimensional polygon is a 2-polytope and a three-dimensional polyhedron is a 3-polytope. In this context, "flat sides" means that the sides of a (k + 1)-polytope consist of k-polytopes that may have (k − 1)-polytopes in ...
Theodore MotzkinTheodore Samuel Motzkin (Hebrew: תיאודור מוצקין; 26 March 1908 – 15 December 1970) was an Israeli-American mathematician.
Lagrange multiplierIn mathematical optimization, the method of Lagrange multipliers is a strategy for finding the local maxima and minima of a function subject to equation constraints (i.e., subject to the condition that one or more equations have to be satisfied exactly by the chosen values of the variables). It is named after the mathematician Joseph-Louis Lagrange.
Mathematical optimizationMathematical 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. It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development of solution methods has been of interest in mathematics for centurie...*As an Amazon Associate I earn from qualifying purchases.