About: Luus–Jaakola

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In computational engineering, Luus–Jaakola (LJ) denotes a heuristic for global optimization of a real-valued function. In engineering use, LJ is not an algorithm that terminates with an optimal solution; nor is it an iterative method that generates a sequence of points that converges to an optimal solution (when one exists). However, when applied to a twice continuously differentiable function, the LJ heuristic is a proper iterative method, that generates a sequence that has a convergent subsequence; for this class of problems, Newton's method is recommended and enjoys a quadratic rate of convergence, while no convergence rate analysis has been given for the LJ heuristic. In practice, the LJ heuristic has been recommended for functions that need be neither convex nor differentiable nor loc

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rdfs:label	Luus–Jaakola (en)
rdfs:comment	In computational engineering, Luus–Jaakola (LJ) denotes a heuristic for global optimization of a real-valued function. In engineering use, LJ is not an algorithm that terminates with an optimal solution; nor is it an iterative method that generates a sequence of points that converges to an optimal solution (when one exists). However, when applied to a twice continuously differentiable function, the LJ heuristic is a proper iterative method, that generates a sequence that has a convergent subsequence; for this class of problems, Newton's method is recommended and enjoys a quadratic rate of convergence, while no convergence rate analysis has been given for the LJ heuristic. In practice, the LJ heuristic has been recommended for functions that need be neither convex nor differentiable nor loc (en)
foaf:depiction
dcterms:subject	Optimization algorithms and methods Heuristic algorithms
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Link from a Wikipage to another Wikipage	Metallurgy Algorithm Pattern search (optimization) Uniform distribution (continuous) Unimodal function Quadratic convergence Optimization (mathematics) Gradient Convex function Lipschitz continuity Subgradient Computational engineering Unit sphere Banach space Optimization algorithms and methods Transformer Global optimization Preconditioner Response surface methodology Heuristic algorithms Chemical engineering Differentiable function Newton's method Mathematical optimization Hypersphere Kantorovich Random optimization Random search Heuristic algorithm
sameAs	Luus–Jaakola Luus–Jaakola Luus–Jaakola
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has abstract	In computational engineering, Luus–Jaakola (LJ) denotes a heuristic for global optimization of a real-valued function. In engineering use, LJ is not an algorithm that terminates with an optimal solution; nor is it an iterative method that generates a sequence of points that converges to an optimal solution (when one exists). However, when applied to a twice continuously differentiable function, the LJ heuristic is a proper iterative method, that generates a sequence that has a convergent subsequence; for this class of problems, Newton's method is recommended and enjoys a quadratic rate of convergence, while no convergence rate analysis has been given for the LJ heuristic. In practice, the LJ heuristic has been recommended for functions that need be neither convex nor differentiable nor locally Lipschitz: The LJ heuristic does not use a gradient or subgradient when one be available, which allows its application to non-differentiable and non-convex problems. Proposed by Luus and Jaakola, LJ generates a sequence of iterates. The next iterate is selected from a sample from a neighborhood of the current position using a uniform distribution. With each iteration, the neighborhood decreases, which forces a subsequence of iterates to converge to a cluster point. Luus has applied LJ in optimal control, transformer design, metallurgical processes, and chemical engineering. (en)
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foaf:isPrimaryTopicOf	wikipedia-en:Luus–Jaakola
is Link from a Wikipage to another Wikipage of	Pattern search (optimization) Derivative-free optimization List of numerical analysis topics Luus-Jaakola method Local search (optimization) Luus-Jaakola Random optimization Random search Luus–Jaakola method Local unimodal sampling
is Wikipage redirect of	Luus-Jaakola method Luus-Jaakola Luus–Jaakola method Local unimodal sampling
is foaf:primaryTopic of	wikipedia-en:Luus–Jaakola

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