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Stochastic Optimization
Stochastic optimization (SO) methods are optimization methods that generate and use random variables. For stochastic problems, the random variables appear in the formulation of the optimization problem itself, which involves random objective functions or random constraints. Stochastic optimization methods also include methods with random iterates. Some stochastic optimization methods use random iterates to solve stochastic problems, combining both meanings of stochastic optimization. Stochastic optimization methods generalize deterministic methods for deterministic problems. Methods for stochastic functions Partly random input data arise in such areas as real-time estimation and control, simulation-based optimization where Monte Carlo simulations are run as estimates of an actual system, and problems where there is experimental (random) error in the measurements of the criterion. In such cases, knowledge that the function values are contaminated by random "noise" leads natural ... [...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 ''n''-th approximation is derived from the previous ones. A specific implementation of an iterative method, including the Algorithm#Termination, termination criteria, is an algorithm of the iterative method. An iterative method is called 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 finite sequence of operations. In the absence of rounding errors, direct methods would deliver an exact solution (for example, solving a linear system of equations A\mathbf=\mathbf by Gaussian elimination). Iterative methods are often the only cho ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elsevier
Elsevier () is a Dutch academic publishing company specializing in scientific, technical, and medical content. Its products include journals such as ''The Lancet'', ''Cell'', the ScienceDirect collection of electronic journals, '' Trends'', the '' Current Opinion'' series, the online citation database Scopus, the SciVal tool for measuring research performance, the ClinicalKey search engine for clinicians, and the ClinicalPath evidence-based cancer care service. Elsevier's products and services also include digital tools for data management, instruction, research analytics and assessment. Elsevier is part of the RELX Group (known until 2015 as Reed Elsevier), a publicly traded company. According to RELX reports, in 2021 Elsevier published more than 600,000 articles annually in over 2,700 journals; as of 2018 its archives contained over 17 million documents and 40,000 e-books, with over one billion annual downloads. Researchers have criticized Elsevier for its high profit marg ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stochastic Tunneling
In numerical analysis, stochastic tunneling (STUN) is an approach to global optimization based on the Monte Carlo method- sampling of the function to be objective minimized in which the function is nonlinearly transformed to allow for easier tunneling among regions containing function minima. Easier tunneling allows for faster exploration of sample space and faster convergence to a good solution. Idea image:stun.jpg, 400px, Schematic one-dimensional test function (black) and STUN effective potential (red & blue), where the minimum indicated by the arrows is the best minimum found so far. All Potential well, wells that lie above the best minimum found are suppressed. If the dynamical process can escape the well around the current minimum estimate it will not be trapped by other local minima that are higher. Wells with deeper minima are enhanced. The dynamical process is accelerated by that. Monte Carlo method-based optimization techniques sample the objective function by randomly ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Anatoly Zhigljavsky
Anatoly Aleksandrovich Zhigljavsky (born 19 November 1953) is a professor of Statistics in the School of Mathematics at Cardiff University. He has authored 12 monographs and over 150 papers in refereed journals. His research interests include stochastic and high-dimensional global optimisation, time series analysis, multivariate data analysis, statistical modeling in market research, probabilistic methods in search and number theory. He is the Director of the Centre for Optimisation and its Applications, an interdisciplinary centre which encourages joint research and applied projects among members of the Schools of Mathematics, Computer Science and Business and Manufacturing Engineering Centre at Cardiff University. It also encourages increased awareness of the rapidly growing field of optimisation through publications, conferences, joint research and student exchange. His books include ''Theory of Global Random Search'', ''Stochastic Global Optimization'', ''Analysis of time s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Random Search
Random search (RS) is a family of numerical optimization methods that do not require the gradient of the problem to be optimized, and RS can hence be used on functions that are not continuous or differentiable. Such optimization methods are also known as direct-search, derivative-free, or black-box methods. Anderson in 1953 reviewed the progress of methods in finding maximum or minimum of problems using a series of guesses distributed with a certain order or pattern in the parameter searching space, e.g. a confounded design with exponentially distributed spacings/steps. This search goes on sequentially on each parameter and refines iteratively on the best guesses from the last sequence. The pattern can be a grid (factorial) search of all parameters, a sequential search on each parameter, or a combination of both. The method was developed to screen the experimental conditions in chemical reactions by a number of scientists listed in Anderson's paper. A MATLAB code reproducing the seq ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dirk Kroese
Dirk Pieter Kroese (born 1963) is a Dutch-Australian mathematician and statistician, and Professor at the University of Queensland. He is known for several contributions to applied probability, kernel density estimation, Monte Carlo methods and Rare event sampling, rare event simulation. He is, with Reuven Rubinstein, a pioneer of the Cross-entropy method, Cross-Entropy (CE) method. Biography Born in Wapenveld (municipality of Heerde), Dirk Kroese received his MSc (Engineer's degree, Netherlands Ingenieur (ir) degree) in 1986 and his Ph.D. (cum laude) in 1990, both from the Department of Applied Mathematics at the University of Twente. His dissertation was entitled ''Stochastic Models in Reliability''. His PhD advisors were Joseph H. A. de Smit and Wilbert C. M. Kallenberg. Part of his PhD research was carried out at Princeton University under the guidance of Erhan Çinlar. He has held teaching and research positions at University of Texas at Austin (1986), Princeton Universit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reuven Rubinstein
Reuven Rubinstein (1938-2012)( he, ראובן רובינשטיין) was an Israeli scientist known for his contributions to Monte Carlo simulation, applied probability, stochastic modeling and stochastic optimization, having authored more than one hundred papers and six books. During his career, Rubinstein has made fundamental and important contributions in these fields and has advanced the theory and application of adaptive importance sampling, rare event simulation, stochastic optimization, sensitivity analysis of simulation-based models, the splitting method, and counting problems concerning NP-complete problems. He is well known as the founder of several breakthrough methods, such as the score function method, stochastic counterpart method and cross-entropy method, which have numerous applications in combinatorial optimization and simulation. His citation index is in the top 5% among his colleagues in operations research and management sciences. His 1981 book "Simulation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cross-entropy Method
The cross-entropy (CE) method is a Monte Carlo method for importance sampling and optimization. It is applicable to both combinatorial and continuous problems, with either a static or noisy objective. The method approximates the optimal importance sampling estimator by repeating two phases:Rubinstein, R.Y. and Kroese, D.P. (2004), The Cross-Entropy Method: A Unified Approach to Combinatorial Optimization, Monte-Carlo Simulation, and Machine Learning, Springer-Verlag, New York . #Draw a sample from a probability distribution. #Minimize the ''cross-entropy'' between this distribution and a target distribution to produce a better sample in the next iteration. Reuven Rubinstein developed the method in the context of ''rare event simulation'', where tiny probabilities must be estimated, for example in network reliability analysis, queueing models, or performance analysis of telecommunication systems. The method has also been applied to the traveling salesman, quadratic assignment, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Springer Verlag
Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing. Originally founded in 1842 in Berlin, it expanded internationally in the 1960s, and through mergers in the 1990s and a sale to venture capitalists it fused with Wolters Kluwer and eventually became part of Springer Nature in 2015. Springer has major offices in Berlin, Heidelberg, Dordrecht, and New York City. History Julius Springer founded Springer-Verlag in Berlin in 1842 and his son Ferdinand Springer grew it from a small firm of 4 employees into Germany's then second largest academic publisher with 65 staff in 1872.Chronology ". Springer Science+Business Media. In 1964, Springer expanded its business internationally, o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Roberto Battiti
Roberto Battiti (born 1961) is an Italian computer scientist, Professor of computer science at the University of Trento, director of the LIONlab (Learning and Intelligent Optimization), and deputy director of the DISI Department (Information Engineering and Computer Science) and delegate for technology transfer. Biography Battiti received the Laurea degree in Physics from the University of Trento in 1985, and the Ph.D. in Computation and Neural Systems from the California Institute of Technology in 1990 under supervision of Geoffrey C. Fox. His main research interests are heuristic algorithms for problem-solving, in particular Reactive Search Optimization, which aims at embodying solvers with internal machine learning techniques, data mining and visualization. Battiti was elected Fellow of the Institute of Electrical and Electronics Engineers in 2009, in recognition of his "contributions to machine learning techniques for intelligent optimization and neural networks", is autho ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reactive Search Optimization
LIONsolver is an integrated software for data mining, business intelligence, analytics, and modeling and reactive business intelligence approach. A non-profit version is also available as LIONoso. LIONsolver is used to build models, visualize them, and improve business and engineering processes. It is a tool for decision making based on data and quantitative model and it can be connected to most databases and external programs. The software is fully integrated with the Grapheur business intelligence and intended for more advanced users. Overview LIONsolver originates from research principles in Reactive Search Optimization advocating the use of self-tuning schemes acting while a software system is running. Learning and Intelligent OptimizatioN refers to the integration of online machine learning schemes into the optimization software, so that it becomes capable of learning from its previous runs and from human feedback. A related approach is that of Programming by Optimiz ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability Collectives
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty."Kendall's Advanced Theory of Statistics, Volume 1: Distribution Theory", Alan Stuart and Keith Ord, 6th Ed, (2009), .William Feller, ''An Introduction to Probability Theory and Its Applications'', (Vol 1), 3rd Ed, (1968), Wiley, . The higher the probability of an event, the more likely it is that the event will occur. A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could also be written as 0.5 or 50%). These conce ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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