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Richard A. Tapia
Richard Alfred Tapia (born March 25, 1939) is an American mathematician and University Professor at Rice University in Houston, Texas, the university's highest academic title. Tapia is the Principal investigator on a $2 million NSF grant (2007-2010) addressing networking for a "minority student or faculty at a majority institution". In 1996, President Bill Clinton awarded Tapia wih the Presidental Award for Mathematics, Science, and Engineering Mentoring. In 2011, President Obama awarded Tapia the National Medal of Science. He is currently the Maxfield and Oshman Professor of Engineering; Associate Director of Graduate Studies, Office of Research and Graduate Studies; and Director of the Center for Excellence and Equity in Education at Rice University. Tapia's mathematical research is centered on mathematical optimization and iterative methods for nonlinear problems, with his current work focused on algorithms for constrained optimization and interior point methods for linear and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Santa Monica, California
Santa Monica (; Spanish language, Spanish: ''Santa Mónica'') is a city in Los Angeles County, California, Los Angeles County, situated along Santa Monica Bay on California's South Coast (California), South Coast. Santa Monica's 2020 United States Census Bureau, U.S. census population was 93,076. Santa Monica is a popular resort town, owing to its climate, beaches, and hospitality industry. It has a diverse economy, hosting headquarters of companies such as Hulu, Activision Blizzard, Universal Music Group, Starz Entertainment Corp., Starz Entertainment, Lionsgate Studios, Illumination (company), Illumination and The Recording Academy. Santa Monica traces its history to Rancho San Vicente y Santa Mónica, granted in 1839 to the Sepúlveda family of California. The rancho was later sold to John Percival Jones, John P. Jones and Robert Symington Baker, Robert Baker, who in 1875, along with his Californio heiress wife Arcadia Bandini de Stearns Baker, founded Santa Monica, which inc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Iterative Method
In computational mathematics, an iterative method is a Algorithm, mathematical procedure that uses an initial value to generate a sequence of improving approximate solutions for a class of problems, in which the ''i''-th approximation (called an "iterate") is derived from the previous ones. A specific implementation with Algorithm#Termination, termination criteria for a given iterative method like gradient descent, hill climbing, Newton's method, or Quasi-Newton method, quasi-Newton methods like Broyden–Fletcher–Goldfarb–Shanno algorithm, BFGS, is an algorithm of an iterative method or a method of successive approximation. An iterative method is called ''Convergent series, convergent'' if the corresponding sequence converges for given initial approximations. A mathematically rigorous convergence analysis of an iterative method is usually performed; however, heuristic-based iterative methods are also common. In contrast, direct methods attempt to solve the problem by a finit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euler–Lagrange Equation
In the calculus of variations and classical mechanics, the Euler–Lagrange equations are a system of second-order ordinary differential equations whose solutions are stationary points of the given action functional. The equations were discovered in the 1750s by Swiss mathematician Leonhard Euler and Italian mathematician Joseph-Louis Lagrange. Because a differentiable functional is stationary at its local extrema, the Euler–Lagrange equation is useful for solving optimization problems in which, given some functional, one seeks the function minimizing or maximizing it. This is analogous to Fermat's theorem in calculus, stating that at any point where a differentiable function attains a local extremum its derivative is zero. In Lagrangian mechanics, according to Hamilton's principle of stationary action, the evolution of a physical system is described by the solutions to the Euler equation for the action of the system. In this context Euler equations are usually called Lagran ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Newton's Method
In numerical analysis, the Newton–Raphson method, also known simply as Newton's method, named after Isaac Newton and Joseph Raphson, is a root-finding algorithm which produces successively better approximations to the roots (or zeroes) of a real-valued function. The most basic version starts with a real-valued function , its derivative , and an initial guess for a root of . If satisfies certain assumptions and the initial guess is close, then x_ = x_0 - \frac is a better approximation of the root than . Geometrically, is the x-intercept of the tangent of the graph of at : that is, the improved guess, , is the unique root of the linear approximation of at the initial guess, . The process is repeated as x_ = x_n - \frac until a sufficiently precise value is reached. The number of correct digits roughly doubles with each step. This algorithm is first in the class of Householder's methods, and was succeeded by Halley's method. The method can also be extended t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Doctor Of Philosophy
A Doctor of Philosophy (PhD, DPhil; or ) is a terminal degree that usually denotes the highest level of academic achievement in a given discipline and is awarded following a course of Postgraduate education, graduate study and original research. The name of the degree is most often abbreviated PhD (or, at times, as Ph.D. in North American English, North America), pronounced as three separate letters ( ). The University of Oxford uses the alternative abbreviation "DPhil". PhDs are awarded for programs across the whole breadth of academic fields. Since it is an earned research degree, those studying for a PhD are required to produce original research that expands the boundaries of knowledge, normally in the form of a Thesis, dissertation, and, in some cases, defend their work before a panel of other experts in the field. In many fields, the completion of a PhD is typically required for employment as a university professor, researcher, or scientist. Definition In the context o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Master Of Arts
A Master of Arts ( or ''Artium Magister''; abbreviated MA or AM) is the holder of a master's degree awarded by universities in many countries. The degree is usually contrasted with that of Master of Science. Those admitted to the degree have typically studied subjects within the scope of the humanities and social sciences, such as history, literature, languages, linguistics, public administration, political science, communication studies, law or diplomacy; however, different universities have different conventions and may also offer the degree for fields typically considered within the natural sciences and mathematics. The degree can be conferred in respect of completing courses and passing examinations, research, or a combination of the two. The degree of Master of Arts traces its origins to the teaching license or of the University of Paris, designed to produce "masters" who were graduate teachers of their subjects. Europe Czech Republic and Slovakia Like all EU membe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bachelor Of Arts
A Bachelor of Arts (abbreviated B.A., BA, A.B. or AB; from the Latin ', ', or ') is the holder of a bachelor's degree awarded for an undergraduate program in the liberal arts, or, in some cases, other disciplines. A Bachelor of Arts degree course is generally completed in three or four years, depending on the country and institution. * Degree attainment typically takes five or more years in Argentina, Brazil, Chile, and Peru. * Degree attainment typically takes four years in Afghanistan, Armenia, Azerbaijan, Bangladesh, Brunei, Bulgaria, Canada (except Quebec), China, Egypt, Finland, Georgia, Ghana, Greece, Hong Kong, Indonesia, India, Iran, Iraq, Ireland, Jamaica, Japan, Kazakhstan, Kenya, Kuwait, Latvia, Lebanon, Lithuania, Malaysia, Mexico, Mongolia, Myanmar, Nepal, the Netherlands, Nigeria, Pakistan, the Philippines, Qatar, Russia, Saudi Arabia, Scotland, Serbia, Singapore, South Africa, South Korea, Spain, Sri Lanka, Taiwan, Thailand, Turkey, Ukraine, the United S ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Horticulture
Horticulture (from ) is the art and science of growing fruits, vegetables, flowers, trees, shrubs and ornamental plants. Horticulture is commonly associated with the more professional and technical aspects of plant cultivation on a smaller and more controlled scale than agronomy. There are various divisions of horticulture because plants are grown for a variety of purposes. These divisions include, but are not limited to: propagation, arboriculture, landscaping, floriculture and turf maintenance. For each of these, there are various professions, aspects, tools used and associated challenges -- each requiring highly specialized skills and knowledge on the part of the horticulturist. Typically, horticulture is characterized as the ornamental, small-scale and non-industrial cultivation of plants; horticulture is distinct from gardening by its emphasis on scientific methods, plant breeding, and technical cultivation practices, while gardening, even at a professional level, tends ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
San Francisco, California
San Francisco, officially the City and County of San Francisco, is a commercial, Financial District, San Francisco, financial, and Culture of San Francisco, cultural center of Northern California. With a population of 827,526 residents as of 2024, San Francisco is the List of California cities by population, fourth-most populous city in the U.S. state of California and the List of United States cities by population, 17th-most populous in the United States. San Francisco has a land area of at the upper end of the San Francisco Peninsula and is the County statistics of the United States, fifth-most densely populated U.S. county. Among U.S. cities proper with over 250,000 residents, San Francisco is ranked first by per capita income and sixth by aggregate income as of 2023. San Francisco anchors the Metropolitan statistical area#United States, 13th-most populous metropolitan statistical area in the U.S., with almost 4.6 million residents in 2023. The larger San Francisco Bay Area ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nonlinear Programming
In mathematics, nonlinear programming (NLP) is the process of solving an optimization problem where some of the constraints are not linear equalities or the objective function is not a linear function. An optimization problem is one of calculation of the extrema (maxima, minima or stationary points) of an objective function over a set of unknown real variables and conditional to the satisfaction of a system of equalities and inequalities, collectively termed constraints. It is the sub-field of mathematical optimization that deals with problems that are not linear. Definition and discussion Let ''n'', ''m'', and ''p'' be positive integers. Let ''X'' be a subset of ''Rn'' (usually a box-constrained one), let ''f'', ''gi'', and ''hj'' be real-valued functions on ''X'' for each ''i'' in and each ''j'' in , with at least one of ''f'', ''gi'', and ''hj'' being nonlinear. A nonlinear programming problem is an optimization problem of the form : \begin \text & f(x) \\ \text ... [...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 and objective 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 polytope. A linear programming algorithm finds a point in the po ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Interior Point Method
Interior-point methods (also referred to as barrier methods or IPMs) are algorithms for solving Linear programming, linear and nonlinear programming, non-linear convex optimization problems. IPMs combine two advantages of previously-known algorithms: * Theoretically, their run-time is Polynomial time, polynomial—in contrast to the simplex method, which has exponential run-time in the worst case. * Practically, they run as fast as the simplex method—in contrast to the ellipsoid method, which has polynomial run-time in theory but is very slow in practice. In contrast to the simplex method which traverses the ''boundary'' of the feasible region, and the ellipsoid method which bounds the feasible region from ''outside'', an IPM reaches a best solution by traversing the ''interior'' of the feasible region—hence the name. History An interior point method was discovered by Soviet mathematician I. I. Dikin in 1967. The method was reinvented in the U.S. in the mid-1980s. In 1984, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
