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Adaptive simulated annealing algorithms address this problem by connecting the cooling schedule to the search progress. Other adaptive approaches such as Thermodynamic Simulated Annealing, [16] automatically adjusts the temperature at each step based on the energy difference between the two states, according to the laws of thermodynamics.
The properties of gradient descent depend on the properties of the objective function and the variant of gradient descent used (for example, if a line search step is used). The assumptions made affect the convergence rate, and other properties, that can be proven for gradient descent. [33]
Indeed, this randomization principle is known to be a simple and effective way to obtain algorithms with almost certain good performance uniformly across many data sets, for many sorts of problems. Stochastic optimization methods of this kind include: simulated annealing by S. Kirkpatrick, C. D. Gelatt and M. P. Vecchi (1983) [10] quantum annealing
By contrast, gradient descent methods can move in any direction that the ridge or alley may ascend or descend. Hence, gradient descent or the conjugate gradient method is generally preferred over hill climbing when the target function is differentiable. Hill climbers, however, have the advantage of not requiring the target function to be ...
Local search is an anytime algorithm; it can return a valid solution even if it's interrupted at any time after finding the first valid solution. Local search is typically an approximation or incomplete algorithm because the search may stop even if the current best solution found is not optimal. This can happen even if termination happens ...
The line-search method first finds a descent direction along which the objective function will be reduced, and then computes a step size that determines how far should move along that direction. The descent direction can be computed by various methods, such as gradient descent or quasi-Newton method. The step size can be determined either ...
Simplex algorithm; Simulated annealing; Simultaneous perturbation stochastic approximation; Social cognitive optimization; Space allocation problem; Space mapping; Special ordered set; Spiral optimization algorithm; Stochastic dynamic programming; Stochastic gradient Langevin dynamics; Stochastic hill climbing; Stochastic programming ...
If reduction of is rapid, a smaller value can be used, bringing the algorithm closer to the Gauss–Newton algorithm, whereas if an iteration gives insufficient reduction in the residual, can be increased, giving a step closer to the gradient-descent direction. Note that the gradient of with respect to equals ([()]).