|
Stochastic Optimization
Stochastic optimization (SO) are optimization methods that generate and use random variables. For stochastic optimization problems, the objective functions or constraints are random. Stochastic optimization also include methods with random iterates. Some hybrid 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 naturally to algorithms that use statistical inference tools to estimate the "true" values of the function and/or make sta ... [...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] |
Scenario Optimization
The scenario approach or scenario optimization approach is a technique for obtaining solutions to robust optimization and chance-constrained optimization problems based on a sample of the constraint (mathematics), constraints. It also relates to inductive reasoning in modeling and decision-making. The technique has existed for decades as a heuristic approach and has more recently been given a systematic theoretical foundation. In Optimization (mathematics), optimization, robustness features translate into constraints that are parameterized by the uncertain elements of the problem. In the scenario method, a solution is obtained by only looking at a random sample of constraints (heuristic approach) called ''scenarios'' and a deeply-grounded theory tells the user how “robust” the corresponding solution is related to other constraints. This theory justifies the use of randomization in robust and chance-constrained optimization. Data-driven optimization At times, scenarios are o ... [...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 simulation. He is, with Reuven Rubinstein, a pioneer of the Cross-Entropy (CE) method. Biography Born in Wapenveld (municipality of Heerde), Dirk Kroese received his MSc ( 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 Çınlar. He has held teaching and research positions at University of Texas at Austin (1986), Princeton University (1988–1989), the University of Twente (1991–1998), ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reuven Rubinstein
Reuven Rubinstein (; 1938–2012) 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 made fundamental and important contributions in these fields and 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, the stochastic counterpart method, and the cross-entropy method, which have numerous applications in combinatorial optimization and simulation. Early life and education Rubinstein was born on August 25, 1938, in Kaunas, Lithuania. In 1960, he received a BSc (unknown subject) and MSc (Electrical Engineering ... [...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, op ... [...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 au ... [...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 a branch of mathematics and statistics concerning events and numerical descriptions of how likely they are to occur. The probability of an event is a number between 0 and 1; the larger the probability, the more likely an event is to occur."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, . This number is often expressed as a percentage (%), ranging from 0% to 100%. 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 concepts have been given an axiomatic mathematical formalizat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Annealing
Quantum annealing (QA) is an optimization process for finding the global minimum of a given objective function over a given set of candidate solutions (candidate states), by a process using quantum fluctuations. Quantum annealing is used mainly for problems where the search space is discrete (combinatorial optimization problems) with many local minima; such as finding the ground state of a spin glass or solving the traveling salesman problem. The term "quantum annealing" was first proposed in 1988 by B. Apolloni, N. Cesa Bianchi and D. De Falco as a quantum-inspired classical algorithm. It was formulated in its present form by T. Kadowaki and H. Nishimori ( ja) in 1998, though an imaginary-time variant without quantum coherence had been discussed by A. B. Finnila, M. A. Gomez, C. Sebenik and J. D. Doll in 1994. Quantum annealing starts from a quantum-mechanical superposition of all possible states (candidate states) with equal weights. Then the system evolves following the time ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Simulated Annealing
Simulated annealing (SA) is a probabilistic technique for approximating the global optimum of a given function. Specifically, it is a metaheuristic to approximate global optimization in a large search space for an optimization problem. For large numbers of local optima, SA can find the global optimum. It is often used when the search space is discrete (for example the traveling salesman problem, the boolean satisfiability problem, protein structure prediction, and job-shop scheduling). For problems where finding an approximate global optimum is more important than finding a precise local optimum in a fixed amount of time, simulated annealing may be preferable to exact algorithms such as gradient descent or branch and bound. The name of the algorithm comes from annealing in metallurgy, a technique involving heating and controlled cooling of a material to alter its physical properties. Both are attributes of the material that depend on their thermodynamic free energy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Randomized Algorithm
A randomized algorithm is an algorithm that employs a degree of randomness as part of its logic or procedure. The algorithm typically uses uniformly random bits as an auxiliary input to guide its behavior, in the hope of achieving good performance in the "average case" over all possible choices of random determined by the random bits; thus either the running time, or the output (or both) are random variables. There is a distinction between algorithms that use the random input so that they always terminate with the correct answer, but where the expected running time is finite (Las Vegas algorithms, for example Quicksort), and algorithms which have a chance of producing an incorrect result ( Monte Carlo algorithms, for example the Monte Carlo algorithm for the MFAS problem) or fail to produce a result either by signaling a failure or failing to terminate. In some cases, probabilistic algorithms are the only practical means of solving a problem. In common practice, randomized alg ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
