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  2. Gradient descent - Wikipedia

    en.wikipedia.org/wiki/Gradient_descent

    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 ]

  3. Barzilai-Borwein method - Wikipedia

    en.wikipedia.org/wiki/Barzilai-Borwein_method

    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 ...

  4. Gradient method - Wikipedia

    en.wikipedia.org/wiki/Gradient_method

    In optimization, a gradient method is an algorithm to solve problems of the form with the search directions defined by the gradient of the function at the current point. Examples of gradient methods are the gradient descent and the conjugate gradient.

  5. Delta rule - Wikipedia

    en.wikipedia.org/wiki/Delta_rule

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  6. Conjugate gradient method - Wikipedia

    en.wikipedia.org/wiki/Conjugate_gradient_method

    A comparison of the convergence of gradient descent with optimal step size (in green) and conjugate vector (in red) for minimizing a quadratic function associated with a given linear system. Conjugate gradient, assuming exact arithmetic, converges in at most n steps, where n is the size of the matrix of the system (here n = 2).

  7. Levenberg–Marquardt algorithm - Wikipedia

    en.wikipedia.org/wiki/Levenberg–Marquardt...

    The LMA interpolates between the Gauss–Newton algorithm (GNA) and the method of gradient descent. The LMA is more robust than the GNA, which means that in many cases it finds a solution even if it starts very far off the final minimum. For well-behaved functions and reasonable starting parameters, the LMA tends to be slower than the GNA.

  8. Powell's method - Wikipedia

    en.wikipedia.org/wiki/Powell's_method

    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. The function must be a real-valued function of a fixed number of real-valued inputs. The caller passes in the initial point.

  9. Descent direction - Wikipedia

    en.wikipedia.org/wiki/Descent_direction

    Numerous methods exist to compute descent directions, all with differing merits, such as gradient descent or the conjugate gradient method. More generally, if P {\displaystyle P} is a positive definite matrix, then p k = − P ∇ f ( x k ) {\displaystyle p_{k}=-P\nabla f(x_{k})} is a descent direction at x k {\displaystyle x_{k}} . [ 1 ]