Wolfe Conditions
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High Quality Content by WIKIPEDIA articles! In the unconstrained minimization problem, the Wolfe conditions are a set of inequalities for performing inexact line search, especially in quasi-Newton methods. In these methods the idea is to find min_x f(mathbf{x}) for some smooth f:mathbb R^ntomathbb R. Each step often involves approximately solving the subproblem min_{alpha} f(mathbf{x}_k + alpha mathbf{p}_k) where mathbf{x}_k is the current best guess, mathbf{p}_k in mathbb R^n is a search direction, and alpha in mathbb R is the step length. Then inexact line searches provide an efficient way…mehr

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High Quality Content by WIKIPEDIA articles! In the unconstrained minimization problem, the Wolfe conditions are a set of inequalities for performing inexact line search, especially in quasi-Newton methods. In these methods the idea is to find min_x f(mathbf{x}) for some smooth f:mathbb R^ntomathbb R. Each step often involves approximately solving the subproblem min_{alpha} f(mathbf{x}_k + alpha mathbf{p}_k) where mathbf{x}_k is the current best guess, mathbf{p}_k in mathbb R^n is a search direction, and alpha in mathbb R is the step length. Then inexact line searches provide an efficient way of computing an acceptable step length that reduces the objective function 'sufficiently', rather than minimizing the objective function over alphainmathbb R^+ exactly. A line search algorithm can use Wolfe conditions as a requirement for any guessed , before finding a new search direction mathbf{p}_k.