Mathematical Description
Hill climbing attempts to maximize (or minimize) a target function, where is a vector of continuous and/or discrete values. At each iteration, hill climbing will adjust a single element in and determine whether the change improves the value of . (Note that this differs from gradient descent methods, which adjust all of the values in at each iteration according to the gradient of the hill.) With hill climbing, any change that improves is accepted, and the process continues until no change can be found to improve the value of . is then said to be "locally optimal".
In discrete vector spaces, each possible value for may be visualized as a vertex in a graph. Hill climbing will follow the graph from vertex to vertex, always locally increasing (or decreasing) the value of, until a local maximum (or local minimum) is reached.
Read more about this topic: Hill Climbing
Famous quotes containing the words mathematical and/or description:
“The most distinct and beautiful statement of any truth must take at last the mathematical form.”
—Henry David Thoreau (1817–1862)
“The next Augustan age will dawn on the other side of the Atlantic. There will, perhaps, be a Thucydides at Boston, a Xenophon at New York, and, in time, a Virgil at Mexico, and a Newton at Peru. At last, some curious traveller from Lima will visit England and give a description of the ruins of St Paul’s, like the editions of Balbec and Palmyra.”
—Horace Walpole (1717–1797)