Luus–Jaakola
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In computational engineering, Luus–Jaakola (LJ) denotes a heuristic for global optimization of a real-valued function.[1] 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.[1] 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,[2] 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.[1]
Luus has applied LJ in optimal control,[3] [4] transformer design,[5] metallurgical processes,[6] and chemical engineering.[7]