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  2. Gradient descent - Wikipedia

    en.wikipedia.org/wiki/Gradient_descent

    Gradient descent with momentum remembers the solution update at each iteration, and determines the next update as a linear combination of the gradient and the previous update. For unconstrained quadratic minimization, a theoretical convergence rate bound of the heavy ball method is asymptotically the same as that for the optimal conjugate ...

  3. Gradient method - Wikipedia

    en.wikipedia.org/wiki/Gradient_method

    In optimization, a gradient method is an algorithm to solve problems of the form min x ∈ R n f ( x ) {\displaystyle \min _{x\in \mathbb {R} ^{n}}\;f(x)} with the search directions defined by the gradient of the function at the current point.

  4. Adjoint state method - Wikipedia

    en.wikipedia.org/wiki/Adjoint_state_method

    The adjoint state method is a numerical method for efficiently computing the gradient of a function or operator in a numerical optimization problem. [1] It has applications in geophysics, seismic imaging, photonics and more recently in neural networks. [2] The adjoint state space is chosen to simplify the physical interpretation of equation ...

  5. Stochastic gradient descent - Wikipedia

    en.wikipedia.org/wiki/Stochastic_gradient_descent

    Stochastic gradient descent competes with the L-BFGS algorithm, [citation needed] which is also widely used. Stochastic gradient descent has been used since at least 1960 for training linear regression models, originally under the name ADALINE. [25] Another stochastic gradient descent algorithm is the least mean squares (LMS) adaptive filter.

  6. Line search - Wikipedia

    en.wikipedia.org/wiki/Line_search

    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 ...

  7. 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 ...

  8. Today's Wordle Hint, Answer for #1270 on Tuesday, December 10 ...

    www.aol.com/todays-wordle-hint-answer-1270...

    If you’re stuck on today’s Wordle answer, we’re here to help—but beware of spoilers for Wordle 1270 ahead. Let's start with a few hints.

  9. Newton's method in optimization - Wikipedia

    en.wikipedia.org/wiki/Newton's_method_in...

    The geometric interpretation of Newton's method is that at each iteration, it amounts to the fitting of a parabola to the graph of () at the trial value , having the same slope and curvature as the graph at that point, and then proceeding to the maximum or minimum of that parabola (in higher dimensions, this may also be a saddle point), see below.