Linjesökning

Linjesökning, also known as line search or line minimization, is a technique used in optimization algorithms to find the optimal step size along a given search direction. It is commonly employed in gradient descent methods and other iterative optimization techniques. The primary goal of linjesökning is to minimize the objective function along the search direction while ensuring that the step size is chosen in a way that maintains the convergence properties of the optimization algorithm.

The process of linjesökning typically involves evaluating the objective function at various points along the search direction and selecting the point that results in the lowest function value. This is often done using a one-dimensional minimization technique, such as the golden-section search or the Brent's method. The chosen step size is then used to update the current solution in the optimization algorithm.

Linjesökning is crucial for the efficiency and convergence of optimization algorithms. By carefully selecting the step size, it helps to balance the trade-off between convergence speed and accuracy. However, the effectiveness of linjesökning can be influenced by the choice of the search direction and the properties of the objective function. In some cases, more sophisticated techniques, such as trust-region methods, may be used to address these challenges.

Overall, linjesökning plays a fundamental role in optimization algorithms by providing a systematic way to determine the optimal step size along the search direction. Its application is widespread in various fields, including machine learning, engineering, and scientific computing, where optimization problems are commonly encountered.