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where C is a contour, and λ is large. One version of the method of steepest descent deforms the contour of integration C into a new path integration C′ so that the following conditions hold: C′ passes through one or more zeros of the derivative g′(z), the imaginary part of g(z) is constant on C′.
The Barzilai-Borwein method [1] is an iterative gradient descent method for unconstrained optimization using either of two step sizes derived from the linear trend of the most recent two iterates. This method, and modifications, are globally convergent under mild conditions, [ 2 ] [ 3 ] and perform competitively with conjugate gradient methods ...
Coordinate descent is an optimization algorithm that successively minimizes along coordinate directions to find the minimum of a function.At each iteration, the algorithm determines a coordinate or coordinate block via a coordinate selection rule, then exactly or inexactly minimizes over the corresponding coordinate hyperplane while fixing all other coordinates or coordinate blocks.
In mathematics, the method of descent is the term coined by the French mathematician Jacques Hadamard as a method for solving a partial differential equation in several real or complex variables, by regarding it as the specialisation of an equation in more variables, constant in the extra parameters.
In (unconstrained) mathematical optimization, a backtracking line search is a line search method to determine the amount to move along a given search direction.Its use requires that the objective function is differentiable and that its gradient is known.
Simple experiments with p=2 showed that SPSA converges in the same number of iterations as FDSA. The latter follows approximately the steepest descent direction, behaving like the gradient method. On the other hand, SPSA, with the random search direction, does not follow exactly the gradient path.
Plot of the Rosenbrock function of two variables. Here a = 1 , b = 100 {\displaystyle a=1,b=100} , and the minimum value of zero is at ( 1 , 1 ) {\displaystyle (1,1)} . In mathematical optimization , the Rosenbrock function is a non- convex function , introduced by Howard H. Rosenbrock in 1960, which is used as a performance test problem for ...
Powell's dog leg method, also called Powell's hybrid method, is an iterative optimisation algorithm for the solution of non-linear least squares problems, introduced in 1970 by Michael J. D. Powell. [1]