|
Zadeh's Rule
In mathematical optimization, Zadeh's rule (also known as the least-entered rule) is an algorithmic refinement of the simplex method for linear programming, linear optimization. The rule was proposed around 1980 by Norman Zadeh (son of Lotfi A. Zadeh), and has entered the folklore of convex optimization since then. Zadeh offered a reward of $1,000 to anyone who can show that the rule admits polynomially many iterations or to prove that there is a family of linear programs on which the pivoting rule requires subexponentially many iterations to find the optimum. Algorithm Zadeh's rule belongs to the family of history-based improvement rules which, during a run of the simplex algorithm, retain supplementary data in addition to the current basis of the linear program. In particular, the rule chooses among all improving variables one which has entered the basis least often, intuitively ensuring that variables that might yield a substantive improvement in the long run but only a small i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Optimization
Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems of sorts 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 centuries. In the more general approach, an optimization problem consists of maxima and minima, maximizing or minimizing a Function of a real variable, real function by systematically choosing Argument of a function, input values from within an allowed set and computing the Value (mathematics), value of the function. The generalization of optimization theory and techniques to other formulations constitutes a large area of applied mathematics. More generally, opti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Simplex Method
In mathematical optimization, Dantzig's simplex algorithm (or simplex method) is a popular algorithm for linear programming. The name of the algorithm is derived from the concept of a simplex and was suggested by T. S. Motzkin. Simplices are not actually used in the method, but one interpretation of it is that it operates on simplicial ''cones'', and these become proper simplices with an additional constraint. The simplicial cones in question are the corners (i.e., the neighborhoods of the vertices) of a geometric object called a polytope. The shape of this polytope is defined by the constraints applied to the objective function. History George Dantzig worked on planning methods for the US Army Air Force during World War II using a desk calculator. During 1946 his colleague challenged him to mechanize the planning process to distract him from taking another job. Dantzig formulated the problem as linear inequalities inspired by the work of Wassily Leontief, however, at that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linear Programming
Linear 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 are represented by linear function#As a polynomial function, 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 mathematical optimization, optimization of a linear objective function, subject to linear equality and linear inequality Constraint (mathematics), constraints. Its feasible region is a convex polytope, which is a set defined as the intersection (mathematics), intersection of finitely many Half-space (geometry), half spaces, each of which is defined by a linear inequality. Its objective function is a real number, real-valued affine function, affine (linear) function defined on this polyhedron. A linear programming algorithm finds a point in the polytope where ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Norman Zadeh
Norman Zada (born Norman Askar Zadeh) is a former adjunct mathematics professor and an entrepreneur. He is the founder of '' Perfect 10'', an adult magazine focusing on women without cosmetic surgery, and runs the United States Investing Competition. Zada is the son of Lotfi Zadeh, the creator of fuzzy logic. Education and early career Zada obtained a PhD in Operations Research at the University of California, Berkeley and worked at IBM. He was an adjunct mathematics Professor at Stanford University, Columbia University, UCLA and University of California, Irvine, writing articles on applied mathematics as well as the 2020 book ''Hold'em Poker Super Strategy''. and the 1974 book ''Winning Poker Systems''. After teaching, he won both backgammon and sports handicapping championships and later became a money manager. In the 1980s he ran a number of financial competitions, including the United States Investing Championship. Zada made headlines in 1996 when he offered $400,000 for anyone ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lotfi A
Lutfi (also spelled Lotfi, Lutvi or Luthfi, ar, لطفي), meaning "kind" or "gracious", may refer to: Given name Lotfi * Lotfi A. Zadeh (1921–2017), Azerbaijani electrical engineer * Lotfi Akalay (born 1943), Moroccan writer * Lotfi Nezzar, Algerian businessman Lutfi, Lütfi * Ahmed Lutfi el-Sayed (1872–1963), Egyptian intellectual * Ali Lutfi Mahmud (1935–2018), Egyptian politician * Lutfi (court official), Ottoman court official * Lutfi Haziri (born 1969), Kosovar politician * Lutfi Lepaja (born 1945), Albanian writer * Lütfi Pasha (died 1564), Ottoman statesman * Lütfi Akadlı (1902–1988), Turkish judge * Lütfi Arıboğan (born 1961), Turkish basketball player * Lütfi Elvan (born 1962), Turkish mining engineer, politician and government minister * Lutfi Kabirova, Tajikistani opera singer * Metin Lütfi Baydar (born 1960), Turkish medical scientist * Mohammed Lutfi Farhat (born 1945), Libyan politician * Mustafa Lutfi al-Manfaluti, Egyptian writer * Ömer Lü ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Super-polynomial Time
In computer science, the time complexity is the computational complexity that describes the amount of computer time it takes to run an algorithm. Time complexity is commonly estimated by counting the number of elementary operations performed by the algorithm, supposing that each elementary operation takes a fixed amount of time to perform. Thus, the amount of time taken and the number of elementary operations performed by the algorithm are taken to be related by a constant factor. Since an algorithm's running time may vary among different inputs of the same size, one commonly considers the worst-case time complexity, which is the maximum amount of time required for inputs of a given size. Less common, and usually specified explicitly, is the average-case complexity, which is the average of the time taken on inputs of a given size (this makes sense because there are only a finite number of possible inputs of a given size). In both cases, the time complexity is generally expressed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Oliver Friedmann
Oliver Friedmann is a German computer scientist and mathematician known for his work on parity games and the simplex algorithm. Friedmann earned his doctorate's degree from the Ludwig Maximilian University of Munich in 2011 under the supervision of Martin Hofmann and Martin Lange. Awards He won the Kleene Award for showing that state-of-the-art policy iteration algorithms for parity games require exponential time in the worst case. He and his coauthors extended the proof techniques to the simplex algorithm and to policy iteration for Markov decision processes. His seminal body of work on lower bounds in convex optimization, leading to a sub-exponential lower bound for Zadeh's rule, was awarded with the Tucker Prize The Tucker Prize for outstanding theses in the area of optimization is sponsored by the Mathematical Optimization Society The Mathematical Optimization Society (MOS), known as the Mathematical Programming Society until 2010, [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Optimization Algorithms And Methods
Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems of sorts 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 centuries. In the more general approach, 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 constitutes a large area of applied mathematics. More generally, optimization includes finding "best available" values of some objective function given a define ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exchange Algorithms
Exchange may refer to: Physics *Gas exchange is the movement of oxygen and carbon dioxide molecules from a region of higher concentration to a region of lower concentration. Places United States * Exchange, Indiana, an unincorporated community * Exchange, Missouri, an unincorporated community * Exchange, Pennsylvania, an unincorporated community * Exchange, West Virginia, an unincorporated community Elsewhere * Exchange Alley, in London, United Kingdom * Exchange District, a historic area in Winnipeg, Manitoba, Canada Business and economy *''Bureau de change'', a business whose customers exchange one currency for another *Cryptocurrency exchange, a business that allows customers to trade cryptocurrencies or digital currencies. *Digital currency exchangers (a.k.a. DCEs or Bitcoin exchanges), businesses that allow customers to trade digital currencies for other assets, such as conventional fiat money, or different digital currencies *Exchange (economics) *Exchange (organized mar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Oriented Matroids
In mathematics, orientability is a property of some topological spaces such as real vector spaces, Euclidean spaces, surfaces, and more generally manifolds that allows a consistent definition of "clockwise" and "counterclockwise". A space is orientable if such a consistent definition exists. In this case, there are two possible definitions, and a choice between them is an orientation of the space. Real vector spaces, Euclidean spaces, and spheres are orientable. A space is non-orientable if "clockwise" is changed into "counterclockwise" after running through some loops in it, and coming back to the starting point. This means that a geometric shape, such as , that moves continuously along such a loop is changed into its own mirror image . A Möbius strip is an example of a non-orientable space. Various equivalent formulations of orientability can be given, depending on the desired application and level of generality. Formulations applicable to general topological manifolds ofte ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
