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Rockafellar
Ralph Tyrrell Rockafellar (born February 10, 1935) is an American mathematician and one of the leading scholars in optimization theory and related fields of analysis and combinatorics. He is the author of four major books including the landmark text "Convex Analysis" (1970), which has been cited more than 27,000 times according to Google Scholar and remains the standard reference on the subject, and "Variational Analysis" (1998, with Roger J-B Wets) for which the authors received the Frederick W. Lanchester Prize from the Institute for Operations Research and the Management Sciences (INFORMS). He is professor emeritus at the departments of mathematics and applied mathematics at the University of Washington, Seattle. Early life and education Ralph Tyrrell Rockafellar was born in Milwaukee, Wisconsin. He is named after his father Ralph Rockafellar, with Tyrrell being his mother’s maiden name. Since his mother was fond of the name Terry, the parents adopted it as a nickname fo ... [...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] |
Oriented Matroid
An oriented matroid is a mathematics, mathematical mathematical structure, structure that abstracts the properties of directed graphs, Vector space, vector arrangements over ordered fields, and Arrangement of hyperplanes, hyperplane arrangements over ordered fields. In comparison, an ordinary (i.e., non-oriented) matroid abstracts the linear independence, dependence properties that are common both to Graph (discrete mathematics), graphs, which are not necessarily ''directed'', and to arrangements of vectors over field (mathematics), fields, which are not necessarily ''ordered''. All oriented matroids have an underlying matroid. Thus, results on ordinary matroids can be applied to oriented matroids. However, the conversion (logic), converse is false; some matroids cannot become an oriented matroid by ''orienting'' an underlying structure (e.g., circuits or independent sets). The distinction between matroids and oriented matroids is discussed further below. Matroids are often usefu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Oriented Matroid
An oriented matroid is a mathematics, mathematical mathematical structure, structure that abstracts the properties of directed graphs, Vector space, vector arrangements over ordered fields, and Arrangement of hyperplanes, hyperplane arrangements over ordered fields. In comparison, an ordinary (i.e., non-oriented) matroid abstracts the linear independence, dependence properties that are common both to Graph (discrete mathematics), graphs, which are not necessarily ''directed'', and to arrangements of vectors over field (mathematics), fields, which are not necessarily ''ordered''. All oriented matroids have an underlying matroid. Thus, results on ordinary matroids can be applied to oriented matroids. However, the conversion (logic), converse is false; some matroids cannot become an oriented matroid by ''orienting'' an underlying structure (e.g., circuits or independent sets). The distinction between matroids and oriented matroids is discussed further below. Matroids are often usefu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Convex Analysis
Convex analysis is the branch of mathematics devoted to the study of properties of convex functions and convex sets, often with applications in convex minimization, a subdomain of optimization theory. Convex sets A subset C \subseteq X of some vector space X is if it satisfies any of the following equivalent conditions: #If 0 \leq r \leq 1 is real and x, y \in C then r x + (1 - r) y \in C. #If 0 is a if holds for any real 0 is called if \operatorname f \neq \varnothing and f(x) > -\infty for x \in \operatorname f. Alternatively, this means that there exists some x in the domain of f at which f(x) \in \mathbb and f is also equal to -\infty. In words, a function is if its domain is not empty, it never takes on the value -\infty, and it also is not identically equal to +\infty. If f : \mathbb^n \to \infty, \infty/math> is a proper convex function then there exist some vector b \in \mathbb^n and some r \in \mathbb such that :f(x) \geq x \cdot b - r for every x where ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Von Neumann
John von Neumann (; hu, Neumann János Lajos, ; December 28, 1903 – February 8, 1957) was a Hungarian-American mathematician, physicist, computer scientist, engineer and polymath. He was regarded as having perhaps the widest coverage of any mathematician of his time and was said to have been "the last representative of the great mathematicians who were equally at home in both pure and applied mathematics". He integrated pure and applied sciences. Von Neumann made major contributions to many fields, including mathematics (foundations of mathematics, measure theory, functional analysis, ergodic theory, group theory, lattice theory, representation theory, operator algebras, matrix theory, geometry, and numerical analysis), physics (quantum mechanics, hydrodynamics, ballistics, nuclear physics and quantum statistical mechanics), economics ( game theory and general equilibrium theory), computing ( Von Neumann architecture, linear programming, numerical meteo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Calculus Of Variation
The calculus of variations (or Variational Calculus) is a field of mathematical analysis that uses variations, which are small changes in functions and functionals, to find maxima and minima of functionals: mappings from a set of functions to the real numbers. Functionals are often expressed as definite integrals involving functions and their derivatives. Functions that maximize or minimize functionals may be found using the Euler–Lagrange equation of the calculus of variations. A simple example of such a problem is to find the curve of shortest length connecting two points. If there are no constraints, the solution is a straight line between the points. However, if the curve is constrained to lie on a surface in space, then the solution is less obvious, and possibly many solutions may exist. Such solutions are known as '' geodesics''. A related problem is posed by Fermat's principle: light follows the path of shortest optical length connecting two points, which depends u ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Werner Fenchel
Moritz Werner Fenchel (; 3 May 1905 – 24 January 1988) was a mathematician known for his contributions to geometry and to optimization theory. Fenchel established the basic results of convex analysis and nonlinear optimization theory which would, in time, serve as the foundation for nonlinear programming. A German-born Jew and early refugee from Nazi suppression of intellectuals, Fenchel lived most of his life in Denmark. Fenchel's monographs and lecture notes are considered influential. Biography Early life and education Fenchel was born on 3 May 1905 in Berlin, Germany, his younger brother was the Israeli film director and architect Heinz Fenchel. Fenchel studied mathematics and physics at the University of Berlin between 1923 and 1928. He wrote his doctorate thesis in geometry (''Über Krümmung und Windung geschlossener Raumkurven'') under Ludwig Bieberbach. Professorship in Germany From 1928 to 1933, Fenchel was Professor E. Landau's Assistant at the Univ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Garrett Birkhoff
Garrett Birkhoff (January 19, 1911 – November 22, 1996) was an American mathematician. He is best known for his work in lattice theory. The mathematician George Birkhoff (1884–1944) was his father. Life The son of the mathematician George David Birkhoff, Garrett was born in Princeton, New Jersey. He began the Harvard University BA course in 1928 after less than seven years of prior formal education. Upon completing his Harvard BA in 1932, he went to Cambridge University to study mathematical physics but switched to studying abstract algebra under Philip Hall. While visiting the University of Munich, he met Carathéodory who pointed him towards two important texts, Van der Waerden on abstract algebra and Speiser on group theory. Birkhoff held no Ph.D., a qualification British higher education did not emphasize at that time, and did not even bother obtaining an M.A. Nevertheless, after being a member of Harvard's Society of Fellows, 1933–36, he spent the rest of h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Francis Clarke (mathematician)
Frank "Francis" H. Clarke (born 30 July 1948, in Montreal) is a Canadian and French mathematician. Biography Francis Clarke graduated in 1969 from McGill University with a B.Sc. degree in 1969 and in 1973 from the University of Washington with a Ph.D. with thesis advisor R. Tyrrell Rockafellar. In 1978 Clarke became a full professor at the University of British Columbia and gave an invited lecture at the International Congress of Mathematicians (ICM) in Helsinki. In 1984 he was appointed director of the ''Centre de Recherches Mathématiques'' (CRM) of the University of Montreal. During the nine years of his directorship, CRM became Canada's leading national research center for mathematics and its applications. The successes of Clarke's directorship included the creation of workshops and postdoctoral fellowships, thematic years, two series of publications, research awards, and an endowment fund. Francis Clarke is also the founding director of the ''Institut des Sciences Mathématiq ... [...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] |
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] |
John Von Neumann Theory Prize
The John von Neumann Theory Prize of the Institute for Operations Research and the Management Sciences (INFORMS) is awarded annually to an individual (or sometimes a group) who has made fundamental and sustained contributions to theory in operations research and the management sciences. The Prize named after mathematician John von Neumann is awarded for a body of work, rather than a single piece. The Prize was intended to reflect contributions that have stood the test of time. The criteria include significance, innovation, depth, and scientific excellence. The award is $5,000, a medallion and a citation. The Prize has been awarded since 1975. The first recipient was George B. Dantzig for his work on linear programming. List of recipients * 2022 Vijay Vazirani * 2021 Alexander Shapiro * 2020 Adrian Lewis * 2019 Dimitris Bertsimas and Jong-Shi Pang * 2018 Dimitri Bertsekas and John Tsitsiklis ** ''for contributions to Parallel and Distributed Computation as well as Neurodynam ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
