Line Minimization

The process of iteratively searching along a vector for the minimum value on the vector is line minimization or line searching. Line minimization can help establish a search direction or verify that the chosen search direction is likely to produce an optimal solution.

Nonlinear programming search algorithms use line minimization to solve the smaller problems of the optimization problem leading to an optimal value for f(x). The search algorithm searches along a vector until it reaches the minimum value on the vector. After the search algorithm reaches the minimum on one vector, the search continues along another vector, usually orthogonal to the first vector. The line search continues along the new vector until reaching its minimum value. The line minimization process continues until the search algorithm finds the optimal solution.