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In optimization, a descent direction is a vector that points towards a local minimum of an objective function :.. Computing by an iterative method, such as line search defines a descent direction at the th iterate to be any such that , <, where , denotes the inner product.
Powell's method, strictly Powell's conjugate direction method, is an algorithm proposed by Michael J. D. Powell for finding a local minimum of a function. The function need not be differentiable, and no derivatives are taken.
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.
Figure 1. Finding the shortest path in a graph using optimal substructure; a straight line indicates a single edge; a wavy line indicates a shortest path between the two vertices it connects (among other paths, not shown, sharing the same two vertices); the bold line is the overall shortest path from start to goal.
If we pick b,c such that the partition a,b,c,z has three equal-length intervals, then the interval shrinks by 2/3 at each iteration, so the method has linear convergence with rate /. Fibonacci search: This is a variant of ternary search in which the points b , c are selected based on the Fibonacci sequence .
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]
By Leah Douglas and Julie Steenhuysen (Reuters) -California's public health department reported a possible case of bird flu in a child with mild respiratory symptoms on Tuesday, but said there was ...
Given a starting position and a search direction , the task of a line search is to determine a step size > that adequately reduces the objective function : (assumed i.e. continuously differentiable), i.e., to find a value of that reduces (+) relative to ().