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Luus–Jaakola

Index Luus–Jaakola

In computational engineering, Luus–Jaakola (LJ) denotes a heuristic for global optimization of a real-valued function. [1]

27 relations: Algorithm, Banach space, Chemical engineering, Computational engineering, Convex function, Differentiable function, Global optimization, Gradient, Heuristic (computer science), Hypersphere, Iterative method, Leonid Kantorovich, Lipschitz continuity, Mathematical optimization, Metallurgy, Newton's method, Optimal control, Pattern search (optimization), Random optimization, Random search, Rate of convergence, Response surface methodology, Subderivative, Transformer, Uniform distribution (continuous), Unimodality, Unit sphere.

Algorithm

In mathematics and computer science, an algorithm is an unambiguous specification of how to solve a class of problems.

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Banach space

In mathematics, more specifically in functional analysis, a Banach space (pronounced) is a complete normed vector space.

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Chemical engineering

Chemical engineering is a branch of engineering that uses principles of chemistry, physics, mathematics and economics to efficiently use, produce, transform, and transport chemicals, materials and energy.

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Computational engineering

Not to be confused with computer engineering. Computational science and engineering (CSE) is a relatively new discipline that deals with the development and application of computational models and simulations, often coupled with high-performance computing, to solve complex physical problems arising in engineering analysis and design (computational engineering) as well as natural phenomena (computational science).

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Convex function

In mathematics, a real-valued function defined on an ''n''-dimensional interval is called convex (or convex downward or concave upward) if the line segment between any two points on the graph of the function lies above or on the graph, in a Euclidean space (or more generally a vector space) of at least two dimensions.

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Differentiable function

In calculus (a branch of mathematics), a differentiable function of one real variable is a function whose derivative exists at each point in its domain.

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Global optimization

Global optimization is a branch of applied mathematics and numerical analysis that deals with the global optimization of a function or a set of functions according to some criteria.

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Gradient

In mathematics, the gradient is a multi-variable generalization of the derivative.

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Heuristic (computer science)

In computer science, artificial intelligence, and mathematical optimization, a heuristic (from Greek εὑρίσκω "I find, discover") is a technique designed for solving a problem more quickly when classic methods are too slow, or for finding an approximate solution when classic methods fail to find any exact solution.

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Hypersphere

In geometry of higher dimensions, a hypersphere is the set of points at a constant distance from a given point called its center.

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Iterative method

In computational mathematics, an iterative method is a mathematical procedure that uses an initial guess 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.

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Leonid Kantorovich

Leonid Vitaliyevich Kantorovich (a) (19 January 19127 April 1986) was a Soviet mathematician and economist, known for his theory and development of techniques for the optimal allocation of resources.

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Lipschitz continuity

In mathematical analysis, Lipschitz continuity, named after Rudolf Lipschitz, is a strong form of uniform continuity for functions.

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Mathematical optimization

In mathematics, computer science and operations research, mathematical optimization or mathematical programming, alternatively spelled optimisation, is the selection of a best element (with regard to some criterion) from some set of available alternatives.

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Metallurgy

Metallurgy is a domain of materials science and engineering that studies the physical and chemical behavior of metallic elements, their inter-metallic compounds, and their mixtures, which are called alloys.

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Newton's method

In numerical analysis, Newton's method (also known as the Newton–Raphson method), named after Isaac Newton and Joseph Raphson, is a method for finding successively better approximations to the roots (or zeroes) of a real-valued function.

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Optimal control

Optimal control theory deals with the problem of finding a control law for a given system such that a certain optimality criterion is achieved.

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Pattern search (optimization)

Pattern search (also known as direct search, derivative-free search, or black-box search) is a family of numerical optimization methods that does not require a gradient.

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Random optimization

Random optimization (RO) is a family of numerical optimization methods that do not require the gradient of the problem to be optimized and RO can hence be used on functions that are not continuous or differentiable.

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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.

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Rate of convergence

In numerical analysis, the speed at which a convergent sequence approaches its limit is called the rate of convergence.

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Response surface methodology

In statistics, response surface methodology (RSM) explores the relationships between several explanatory variables and one or more response variables.

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Subderivative

In mathematics, the subderivative, subgradient, and subdifferential generalize the derivative to functions which are not differentiable.

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Transformer

A transformer is a static electrical device that transfers electrical energy between two or more circuits through electromagnetic induction.

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Uniform distribution (continuous)

In probability theory and statistics, the continuous uniform distribution or rectangular distribution is a family of symmetric probability distributions such that for each member of the family, all intervals of the same length on the distribution's support are equally probable.

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Unimodality

In mathematics, unimodality means possessing a unique mode.

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Unit sphere

In mathematics, a unit sphere is the set of points of distance 1 from a fixed central point, where a generalized concept of distance may be used; a closed unit ball is the set of points of distance less than or equal to 1 from a fixed central point.

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Local unimodal sampling, Luus-Jaakola.

References

[1] https://en.wikipedia.org/wiki/Luus–Jaakola

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