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Relaxation (approximation)
In mathematical optimization and related fields, relaxation is a modeling strategy. A relaxation is an approximation of a difficult problem by a nearby problem that is easier to solve. A solution of the relaxed problem provides information about the original problem. For example, a linear programming relaxation of an integer programming problem removes the integrality constraint and so allows non-integer rational solutions. A Lagrangian relaxation of a complicated problem in combinatorial optimization penalizes violations of some constraints, allowing an easier relaxed problem to be solved. Relaxation techniques complement or supplement branch and bound algorithms of combinatorial optimization; linear programming and Lagrangian relaxations are used to obtain bounds in branch-and-bound algorithms for integer programming. The modeling strategy of relaxation should not be confused with iterative methods of relaxation, such as successive over-relaxation (SOR); iterative methods of ... [...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, op ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Successive Over-relaxation
In numerical linear algebra, the method of successive over-relaxation (SOR) is a variant of the Gauss–Seidel method for solving a linear system of equations, resulting in faster convergence. A similar method can be used for any slowly converging iterative process. It was devised simultaneously by David M. Young Jr. and by Stanley P. Frankel in 1950 for the purpose of automatically solving linear systems on digital computers. Over-relaxation methods had been used before the work of Young and Frankel. An example is the method of Lewis Fry Richardson, and the methods developed by R. V. Southwell. However, these methods were designed for computation by human calculators, requiring some expertise to ensure convergence to the solution which made them inapplicable for programming on digital computers. These aspects are discussed in the thesis of David M. Young Jr. Formulation Given a square system of ''n'' linear equations with unknown x: :A\mathbf x = \mathbf b where: :A=\beg ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Relaxation (approximation)
In mathematical optimization and related fields, relaxation is a modeling strategy. A relaxation is an approximation of a difficult problem by a nearby problem that is easier to solve. A solution of the relaxed problem provides information about the original problem. For example, a linear programming relaxation of an integer programming problem removes the integrality constraint and so allows non-integer rational solutions. A Lagrangian relaxation of a complicated problem in combinatorial optimization penalizes violations of some constraints, allowing an easier relaxed problem to be solved. Relaxation techniques complement or supplement branch and bound algorithms of combinatorial optimization; linear programming and Lagrangian relaxations are used to obtain bounds in branch-and-bound algorithms for integer programming. The modeling strategy of relaxation should not be confused with iterative methods of relaxation, such as successive over-relaxation (SOR); iterative methods of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Roger J-B Wets
Roger Jean-Baptiste Robert Wets (born February 1937) is a "pioneer" in stochastic programming and a leader in variational analysis who publishes as Roger J-B Wets. His research, expositions, graduate students, and his collaboration with R. Tyrrell Rockafellar have had a profound influence on optimization theory, computations, and applications. Since 2009, Wets has been a distinguished research professor at the mathematics department of the University of California, Davis. Schooling and positions Roger Wets attended high school in Belgium, after which he worked for his family while earning his ''Licence'' in applied economics from Université de Bruxelles (Brussels, Belgium) in 1961. He was encouraged by Jacques H. Drèze to study optimization with George Dantzig at the program in operations research at the University of California, Berkeley. Dantzig and mathematician–statistician David Blackwell jointly supervised Wets's dissertation. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Claude Lemaréchal
Claude Lemaréchal is a French applied mathematician, and former senior researcher (''directeur de recherche'') at INRIA near Grenoble, France. In mathematical optimization, Claude Lemaréchal is known for his work in numerical methods for nonlinear optimization, especially for problems with nondifferentiable kinks. Lemaréchal and Philip Wolfe pioneered bundle methods of descent for convex minimization.Citation of Claude Lemaréchal for the Prize in 1994 in ''Optima'', Issue 44 (1994) pages 4-5. Awards In 1994, Claude Lemaréchal and |
James B
James is a common English language surname and given name: *James (name), the typically masculine first name James * James (surname), various people with the last name James James or James City may also refer to: People * King James (other), various kings named James * Saint James (other) * James (musician) * James, brother of Jesus Places Canada * James Bay, a large body of water * James, Ontario United Kingdom * James College, a college of the University of York United States * James, Georgia, an unincorporated community * James, Iowa, an unincorporated community * James City, North Carolina * James City County, Virginia ** James City (Virginia Company) ** James City Shire * James City, Pennsylvania * St. James City, Florida Arts, entertainment, and media * ''James'' (2005 film), a Bollywood film * ''James'' (2008 film), an Irish short film * ''James'' (2022 film), an Indian Kannada-language film * James the Red Engine, a character in ''Tho ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thomas L
Thomas may refer to: People * List of people with given name Thomas * Thomas (name) * Thomas (surname) * Saint Thomas (other) * Thomas Aquinas (1225–1274) Italian Dominican friar, philosopher, and Doctor of the Church * Thomas the Apostle * Thomas (bishop of the East Angles) (fl. 640s–650s), medieval Bishop of the East Angles * Thomas (Archdeacon of Barnstaple) (fl. 1203), Archdeacon of Barnstaple * Thomas, Count of Perche (1195–1217), Count of Perche * Thomas (bishop of Finland) (1248), first known Bishop of Finland * Thomas, Earl of Mar (1330–1377), 14th-century Earl, Aberdeen, Scotland Geography Places in the United States * Thomas, Illinois * Thomas, Indiana * Thomas, Oklahoma * Thomas, Oregon * Thomas, South Dakota * Thomas, Virginia * Thomas, Washington * Thomas, West Virginia * Thomas County (other) * Thomas Township (other) Elsewhere * Thomas Glacier (Greenland) Arts, entertainment, and media * ''Thomas'' (Burton n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ravindra K
People * Ravindra Jain (1944–2015), an Indian music composer and lyricist * Ravindra Mahajani, an Indian film actor *Ravindra Pushpakumara (b. 1975), a Sri Lankan cricketer * Ravindra Randeniya, a Sri Lankan actor and politician *Ravindra Khattree (b. 1959), an Indian born statistician and professor of statistics at Oakland University * Ravindra Kelekar (1925–2010), a noted Indian writer * Ravindra Jadeja *Paritala Ravindra (1958–2005), a political leader in the Rayalaseema region of Andhra Pradesh, India * Ravindra Mankani (b. 1956), a veteran actor who is noted for his work in many a daily soaps, plays and films *Ravindra Patil (b. 1955), a politician from Jalgaon * Ravindra Prabhat (b. 1969), an Indian poet, writer & journalist *Ravindra Lakmal (b. 1981), a Sri Lankan cricketer * Ravindra Samaraweera, a Sri Lankan politician and a member of the Parliament of Sri Lanka * Ravindra Mhatre, an Indian diplomat in UK who was kidnapped and later murdered in Birmingham in 1984 * Rav ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Margaret H
Margaret is a female first name, derived via French () and Latin () from grc, μαργαρίτης () meaning " pearl". The Greek is borrowed from Persian. Margaret has been an English name since the 11th century, and remained popular throughout the Middle Ages. It became less popular between the 16th century and 18th century, but became more common again after this period, becoming the second-most popular female name in the United States in 1903. Since this time, it has become less common, but was still the ninth-most common name for women of all ages in the United States as of the 1990 census. Margaret has many diminutive forms in many different languages, including Maggie, Madge, Daisy, Margarete, Marge, Margo, Margie, Marjorie, Meg, Megan, Rita, Greta, Gretchen, and Peggy. Name variants Full name * ( Irish) * ( Irish) * ( Dutch), ( German), (Swedish) * ( English) Diminutives * ( English) * ( English) First half * (French) * (Welsh) Second half * ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Donald Goldfarb
Donald Goldfarb (born August 14, 1941 in New York City) is an American mathematician, best known for his works in mathematical optimization and numerical analysis. Goldfarb studied Chemical Engineering at Cornell University, earning a BSChE in 1963. He obtained an M.S. from Princeton University in 1965, and a doctorate in 1966."Donakd Gokdfarb fsvulty homepage" Columbia University School of Engineering. Accessed February 16, 2022. After getting his Ph.D., Goldfarb spent two years as a post-doc at the Courant Institute in New York City. In 1968, he co-founded the CS Department at |
Robert B
The name Robert is an ancient Germanic given name, from Proto-Germanic "fame" and "bright" (''Hrōþiberhtaz''). Compare Old Dutch ''Robrecht'' and Old High German ''Hrodebert'' (a compound of '' Hruod'' ( non, Hróðr) "fame, glory, honour, praise, renown" and ''berht'' "bright, light, shining"). It is the second most frequently used given name of ancient Germanic origin. It is also in use as a surname. Another commonly used form of the name is Rupert. After becoming widely used in Continental Europe it entered England in its Old French form ''Robert'', where an Old English cognate form (''Hrēodbēorht'', ''Hrodberht'', ''Hrēodbēorð'', ''Hrœdbœrð'', ''Hrœdberð'', ''Hrōðberχtŕ'') had existed before the Norman Conquest. The feminine version is Roberta. The Italian, Portuguese, and Spanish form is Roberto. Robert is also a common name in many Germanic languages, including English, German, Dutch, Norwegian, Swedish, Scots, Danish, and Icelandic. It can ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Surrogate Duality
A surrogate is a substitute or deputy for another person in a specific role and may refer to: Relationships * Surrogacy, an arrangement where a woman agrees to carry and give birth to a child for another person who will become its parent at birth * Sexual surrogate, in sexual therapy * Surrogate marriage, a custom in Zulu culture Economics *Ersatz, an artificial replacement differing in kind from and inferior in quality to what it replaces. *Surrogation, a psychological phenomenon in management science Arts * Author surrogate or audience surrogate, reciprocal literary techniques * The Surrogates, a comic book series * ''Surrogates'' (film), a 2009 film based on the comic book series * ''The Surrogate'' (1984 film), a Canadian erotic film starring Art Hindle * ''The Surrogate'' (1995 film), a TV movie starring Alyssa Milano * ''The Surrogate'' (2020 film), an American LGBT-related Independent drama film *''The Surrogate'', original title of '' The Sessions'', a 2012 film ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
