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Relaxation (approximation)
In mathematical optimization and related fields, relaxation is a mathematical model, 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 method, relaxation, such as successive over-re ... [...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 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 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. Optimization problems Opti ... [...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=\be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Relaxation (approximation)
In mathematical optimization and related fields, relaxation is a mathematical model, 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 method, relaxation, such as successive over-re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Roger J-B Wets
Roger Jean-Baptiste Robert Wets (February 1937 – April 1, 2025) was a Belgian stochastic programming and a leader in calculus of variations, 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 ''Licenciate#Belgium, Licence'' in applied economics from Université de Bruxelles (Brussels, Belgium) in 1961. He was encouraged by Jacques H. Drèze to study mathematical optimization, optimization with George Dantzig at the program in operations research at the University of California, Berkeley. Dantzig and mathematician–statistician David ... [...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 George Dantzig Prize in 1994 in ''Optima'', Issue 44 (1994) pages 4-5. Awards In 1994, Claude Lemaréchal and Roger J-B Wets were each ...[...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
James B
James may refer to: People * James (given name) * James (surname) * James (musician), aka Faruq Mahfuz Anam James, (born 1964), Bollywood musician * James, brother of Jesus * King James (other), various kings named James * Prince James (other) * Saint James (other) 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 Film and television * ''James'' (2005 film), a Bollywood film * ''James'' (2008 film), an Irish short film * ''James'' (2022 film), an Indian Kannada-language film * "James", a television episode of ''Adventure Time'' Music * James (band), a band from Manchester ** ''James'', ... [...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, Idaho * Thomas, Illinois * 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 and entertainment *Thomas (Burton novel), ''Thomas'' (Burton novel) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ravindra K
Ravinder or Ravindra is an Indian given name. A short form of the name is Ravi. Notable people with this name include: * Rachin Ravindra, New Zealand cricketer * Ravinder Baliala, member of the Haryana Legislative Assembly * Ravinder Bhalla, American civil rights lawyer, and mayor of Hoboken, New Jersey * Ravinder Bhogal, restaurateur, food writer, and chef * Ravinder Bopara, cricketer * Ravinder Chadha, cricketer * Ravinder Dhallan, chairman and chief executive officer of Ravgen * Ravinder Goswami, professor at the department of endocrinology and metabolism at the All India Institute of Medical Sciences, Delhi * Ravinder Grewal, singer and actor * Ravinder K. Jain, physicist, and academic from the University of New Mexico * Ravinder Kapoor, film actor popularly known as Goga Kapoor * Ravinder Khatri, Greco-Roman wrestler * Ravinder Kumar, historian * Ravinder Kumar, Member of the Legislative Assembly of India * Ravinder Kumar, serial killer * Ravinder Kumar Dhir, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Margaret H
Margaret is a feminine given name, which means "pearl". It is of Latin origin, via Ancient Greek and ultimately from Old Iranian. It has been an English name since the 11th century, and remained popular throughout the Middle Ages. It became less popular between the 16th 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 languages, including Daisy, Greta, Gretchen, Maggie, Madge, Maisie, Marge, Margie, Margo, Margot, Marnie, Meg, Megan, Molly, Peggy, and Rita. Etymology Margaret is derived via French () and Latin () from (), via Persian ''murwārīd'', meaning "pearl". Margarita (given name) traces the etymology further as مروارید, ''morvārīd'' in modern Persian, derived fr ... [...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. Biography 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 [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 ''Hrōþ, Hruod'' () "fame, glory, honour, praise, renown, godlike" and ''berht'' "bright, light, shining"). It is the second most frequently used given name of ancient Germanic origin.Reaney & Wilson, 1997. ''Dictionary of English Surnames''. Oxford University Press. It is also in use Robert (surname), as a surname. Another commonly used form of the name is Rupert (name), Rupert. After becoming widely used in Continental Europe, the name 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 (given name), Roberta. The Italian, Portuguese, and Spanish form is Roberto (given name), ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics Of Operations Research
''Mathematics of Operations Research'' is a quarterly peer-reviewed scientific journal established in February 1976. It focuses on areas of mathematics relevant to the field of operations research such as continuous optimization, discrete optimization, game theory, machine learning, simulation methodology, and stochastic models. The journal is published by INFORMS (Institute for Operations Research and the Management Sciences). the journal has a 2017 impact factor of 1.078. History The journal was established in 1976. The founding editor-in-chief was Arthur F. Veinott Jr. (Stanford University). He served until 1980, when the position was taken over by Stephen M. Robinson, who held the position until 1986. Erhan Cinlar served from 1987 to 1992, and was followed by Jan Karel Lenstra (1993-1998). Next was Gérard Cornuéjols (1999-2003) and Nimrod Megiddo (2004-2009). Finally came Uri Rothblum (2009-2012), Jim Dai (2012-2018), and the current editor-in-chief Katya Scheinberg (20 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
