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KNITRO
Artelys Knitro is a commercial software package for solving large scale nonlinear mathematical optimization problems. KNITRO – (the original solver name) short for "Nonlinear Interior point Trust Region Optimization" (the "K" is silent) – was co-created by Richard Waltz, Jorge Nocedal, Todd Plantenga and Richard Byrd. It was first introduced in 2001, as a derivative of academic research at Northwestern University (through Ziena Optimization LLC), and has since been continually improved by developers at Artelys. Optimization problems must be presented to Knitro in mathematical form, and should provide a way of computing function derivatives using sparse matrices (Knitro can compute derivatives approximation but in most cases providing the exact derivatives is beneficial). An often easier approach is to develop the optimization problem in an algebraic modeling language. The modeling environment computes function derivatives, and Knitro is called as a "solver" from within the en ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jorge Nocedal
Jorge Nocedal (born 1952) is a applied mathematician, computer scientist and the Walter P. Murphy professor at Northwestern University who in 2017 received the John Von Neumann Theory Prize. He was elected a member of the National Academy of Engineering in 2020. Nocedal specializes in nonlinear optimization, both in the deterministic and stochastic setting. The motivation for his current algorithmic and theoretical research stems from applications in image and speech recognition, recommendation systems, and search engines. In the past, he has also worked on equilibrium problems with application in robotics, traffics, and games, optimization applications in finance, as well as PDE-constrained optimization. Biography Nocedal was born and raised in Mexico. He obtained a B.Sc. in physics from the National University of Mexico in 1974. From 1974 to 1978, Nocedal studied at Rice University where he obtained a PhD in mathematical sciences under the supervision of Richard A. Tapia. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proprietary Software
Proprietary software is software that is deemed within the free and open-source software to be non-free because its creator, publisher, or other rightsholder or rightsholder partner exercises a legal monopoly afforded by modern copyright and intellectual property law to exclude the recipient from freely sharing the software or modifying it, and—in some cases, as is the case with some patent-encumbered and EULA-bound software—from making use of the software on their own, thereby restricting his or her freedoms. It is often contrasted with open-source or free software. For this reason, it is also known as non-free software or closed-source software. Types Origin Until the late 1960s computers—large and expensive mainframe computers, machines in specially air-conditioned computer rooms—were usually leased to customers rather than sold. Service and all software available were usually supplied by manufacturers without separate charge until 1969. Computer vendors ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algorithm
In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can perform automated deductions (referred to as automated reasoning) and use mathematical and logical tests to divert the code execution through various routes (referred to as automated decision-making). Using human characteristics as descriptors of machines in metaphorical ways was already practiced by Alan Turing with terms such as "memory", "search" and "stimulus". In contrast, a Heuristic (computer science), heuristic is an approach to problem solving that may not be fully specified or may not guarantee correct or optimal results, especially in problem domains where there is no well-defined correct or optimal result. As an effective method, an algorithm ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robert R
Robert Lee Rayford (February 3, 1953 – May 15 1969), sometimes identified as Robert R. due to his age, was an American teenager from Missouri who has been suggested to represent the earliest confirmed case of HIV/AIDS in North America based on evidence which was published in 1988 in which the authors claimed that medical evidence indicated that he was "infected with a virus closely related or identical to human immunodeficiency virus type 1." Rayford died of pneumonia, but his other symptoms baffled the doctors who treated him. A study published in 1988 reported the detection of antibodies against HIV. Results of testing for HIV genetic material were reported once at a scientific conference in Australia in 1999; however, the data has never been published in a peer-reviewed medical or scientific journal. Background Robert Rayford was born on February 3, 1953, in St. Louis, Missouri to Constance Rayford (September 12, 1931 – April 3, 2011) and Joseph Benny Bell (March 24, 1 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Springer Publishing
Springer Publishing Company is an American publishing company of academic journals and books, focusing on the fields of nursing, gerontology, psychology, social work, counseling, public health, and rehabilitation (neuropsychology). It was established in 1951 by Bernhard Springer, a great-grandson of Julius Springer, and is based in Midtown Manhattan, New York City. History Springer Publishing Company was founded in 1950 by Bernhard Springer, the Berlin-born great-grandson of Julius Springer, who founded Springer-Verlag (now Springer Science+Business Media). Springer Publishing's first landmark publications included ''Livestock Health Encyclopedia'' by R. Seiden and the 1952 ''Handbook of Cardiology for Nurses''. The company's books soon branched into other fields, including medicine and psychology. Nursing publications grew rapidly in number, as Modell's ''Drugs in Current Use'', a small annual paperback, sold over 150,000 copies over several editions. Solomon Garb's ''Labor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
ARM Architecture
ARM (stylised in lowercase as arm, formerly an acronym for Advanced RISC Machines and originally Acorn RISC Machine) is a family of reduced instruction set computer (RISC) instruction set architectures for computer processors, configured for various environments. Arm Ltd. develops the architectures and licenses them to other companies, who design their own products that implement one or more of those architectures, including system on a chip (SoC) and system on module (SOM) designs, that incorporate different components such as memory, interfaces, and radios. It also designs cores that implement these instruction set architectures and licenses these designs to many companies that incorporate those core designs into their own products. There have been several generations of the ARM design. The original ARM1 used a 32-bit internal structure but had a 26-bit address space that limited it to 64 MB of main memory. This limitation was removed in the ARMv3 series, which ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Global Minimum
In mathematical analysis, the maxima and minima (the respective plurals of maximum and minimum) of a function, known collectively as extrema (the plural of extremum), are the largest and smallest value of the function, either within a given range (the ''local'' or ''relative'' extrema), or on the entire domain (the ''global'' or ''absolute'' extrema). Pierre de Fermat was one of the first mathematicians to propose a general technique, adequality, for finding the maxima and minima of functions. As defined in set theory, the maximum and minimum of a set are the greatest and least elements in the set, respectively. Unbounded infinite sets, such as the set of real numbers, have no minimum or maximum. Definition A real-valued function ''f'' defined on a domain ''X'' has a global (or absolute) maximum point at ''x''∗, if for all ''x'' in ''X''. Similarly, the function has a global (or absolute) minimum point at ''x''∗, if for all ''x'' in ''X''. The value of the function at a m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Feasible Region
In mathematical optimization, a feasible region, feasible set, search space, or solution space is the set of all possible points (sets of values of the choice variables) of an optimization problem that satisfy the problem's constraints, potentially including inequalities, equalities, and integer constraints. This is the initial set of candidate solutions to the problem, before the set of candidates has been narrowed down. For example, consider the problem of minimizing the function x^2+y^4 with respect to the variables x and y, subject to 1 \le x \le 10 and 5 \le y \le 12. \, Here the feasible set is the set of pairs (''x'', ''y'') in which the value of ''x'' is at least 1 and at most 10 and the value of ''y'' is at least 5 and at most 12. The feasible set of the problem is separate from the objective function, which states the criterion to be optimized and which in the above example is x^2+y^4. In many problems, the feasible set reflects a constraint that one or more ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Active Set Method
In mathematical optimization, the active-set method is an algorithm used to identify the active constraints in a set of inequality constraints. The active constraints are then expressed as equality constraints, thereby transforming an inequality-constrained problem into a simpler equality-constrained subproblem. An optimization problem is defined using an objective function to minimize or maximize, and a set of constraints : g_1(x) \ge 0, \dots, g_k(x) \ge 0 that define the feasible region, that is, the set of all ''x'' to search for the optimal solution. Given a point x in the feasible region, a constraint : g_i(x) \ge 0 is called active at x_0 if g_i(x_0) = 0, and inactive at x if g_i(x_0) > 0. Equality constraints are always active. The active set at x_0 is made up of those constraints g_i(x_0) that are active at the current point . The active set is particularly important in optimization theory, as it determines which constraints will influence the final result of optim ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Interior Point Method
Interior-point methods (also referred to as barrier methods or IPMs) are a certain class of algorithms that solve linear and nonlinear convex optimization problems. An interior point method was discovered by Soviet mathematician I. I. Dikin in 1967 and reinvented in the U.S. in the mid-1980s. In 1984, Narendra Karmarkar developed a method for linear programming called Karmarkar's algorithm, which runs in provably polynomial time and is also very efficient in practice. It enabled solutions of linear programming problems that were beyond the capabilities of the simplex method. Contrary to the simplex method, it reaches a best solution by traversing the interior of the feasible region. The method can be generalized to convex programming based on a self-concordant barrier function used to encode the convex set. Any convex optimization problem can be transformed into minimizing (or maximizing) a linear function over a convex set by converting to the epigraph form. The idea of encodi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nonlinear Optimization
In mathematics, nonlinear programming (NLP) is the process of solving an optimization problem where some of the constraints or the objective function are nonlinear. 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. Applicability A typical non-convex problem is that of optimizing transportation costs by selection from a set of transportation methods, one or more of which exhibit economies of scale, with various connectivities and capacity constraints. An example would be petroleum product transport given a selection or combination of pipeline, rail tanker, road tanker, river barge, or coastal tankship. Owing to economic batch size the cost functions may have discontin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cross-platform
In computing, cross-platform software (also called multi-platform software, platform-agnostic software, or platform-independent software) is computer software that is designed to work in several computing platforms. Some cross-platform software requires a separate build for each platform, but some can be directly run on any platform without special preparation, being written in an interpreted language or compiled to portable bytecode for which the interpreters or run-time packages are common or standard components of all supported platforms. For example, a cross-platform application may run on Microsoft Windows, Linux, and macOS. Cross-platform software may run on many platforms, or as few as two. Some frameworks for cross-platform development are Codename One, Kivy, Qt, Flutter, NativeScript, Xamarin, Phonegap, Ionic, and React Native. Platforms ''Platform'' can refer to the type of processor (CPU) or other hardware on which an operating system (OS) or application runs, t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
