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17 relations: Backtracking line search, Conjugate gradient method, Descent direction, Golden-section search, Gradient descent, Iteration, Loss function, Mathematical optimization, Maxima and minima, Nelder–Mead method, Newton's method in optimization, Pattern search (optimization), Quasi-Newton method, Secant method, Simulated annealing, Trust region, Wolfe conditions.
Backtracking line search
In (unconstrained) minimization, a backtracking line search, a search scheme based on the Armijo–Goldstein condition, is a line search method to determine the maximum amount to move along a given search direction.
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Conjugate gradient method
In mathematics, the conjugate gradient method is an algorithm for the numerical solution of particular systems of linear equations, namely those whose matrix is symmetric and positive-definite.
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Descent direction
In optimization, a descent direction is a vector \mathbf\in\mathbb R^n that, in the sense below, moves us closer towards a local minimum \mathbf^* of our objective function f:\mathbb R^n\to\mathbb R. Suppose we are computing \mathbf^* by an iterative method, such as line search.
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Golden-section search
The golden-section search is a technique for finding the extremum (minimum or maximum) of a strictly unimodal function by successively narrowing the range of values inside which the extremum is known to exist.
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Gradient descent
Gradient descent is a first-order iterative optimization algorithm for finding the minimum of a function.
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Iteration
Iteration is the act of repeating a process, to generate a (possibly unbounded) sequence of outcomes, with the aim of approaching a desired goal, target or result.
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Loss function
In mathematical optimization, statistics, econometrics, decision theory, machine learning and computational neuroscience, a loss function or cost function is a function that maps an event or values of one or more variables onto a real number intuitively representing some "cost" associated with the event.
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Mathematical optimization
In mathematics, computer science and operations research, mathematical optimization or mathematical programming, alternatively spelled optimisation, is the selection of a best element (with regard to some criterion) from some set of available alternatives.
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Maxima and minima
In mathematical analysis, the maxima and minima (the respective plurals of maximum and minimum) of a function, known collectively as extrema (the plural of extremum), are the largest and smallest value of the function, either within a given range (the local or relative extrema) or on the entire domain of a function (the global or absolute extrema).
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Nelder–Mead method
The Nelder–Mead method or downhill simplex method or amoeba method is a commonly applied numerical method used to find the minimum or maximum of an objective function in a multidimensional space.
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Newton's method in optimization
In calculus, Newton's method is an iterative method for finding the roots of a differentiable function (i.e. solutions to the equation). In optimization, Newton's method is applied to the derivative of a twice-differentiable function to find the roots of the derivative (solutions to), also known as the stationary points of.
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Pattern search (optimization)
Pattern search (also known as direct search, derivative-free search, or black-box search) is a family of numerical optimization methods that does not require a gradient.
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Quasi-Newton method
Quasi-Newton methods are methods used to either find zeroes or local maxima and minima of functions, as an alternative to Newton's method.
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Secant method
In numerical analysis, the secant method is a root-finding algorithm that uses a succession of roots of secant lines to better approximate a root of a function f. The secant method can be thought of as a finite-difference approximation of Newton's method.
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Simulated annealing
Simulated annealing (SA) is a probabilistic technique for approximating the global optimum of a given function.
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Trust region
Trust region is a term used in mathematical optimization to denote the subset of the region of the objective function that is approximated using a model function (often a quadratic).
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Wolfe conditions
In the unconstrained minimization problem, the Wolfe conditions are a set of inequalities for performing inexact line search, especially in quasi-Newton methods, first published by Philip Wolfe in 1969.
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