On search directions for minimization algorithms
MJD Powell - Mathematical programming, 1973 - Springer
MJD Powell
Mathematical programming, 1973•SpringerSome examples are given of differentiable functions of three variables, having the property
that if they are treated by the minimization algorithm that searches along the coordinate
directions in sequence, then the search path tends to a closed loop. On this loop the
gradient of the objective function is bounded away from zero. We discuss the relevance of
these examples to the problem of proving general convergence theorems for minimization
algorithms that use search directions.
that if they are treated by the minimization algorithm that searches along the coordinate
directions in sequence, then the search path tends to a closed loop. On this loop the
gradient of the objective function is bounded away from zero. We discuss the relevance of
these examples to the problem of proving general convergence theorems for minimization
algorithms that use search directions.
Abstract
Some examples are given of differentiable functions of three variables, having the property that if they are treated by the minimization algorithm that searches along the coordinate directions in sequence, then the search path tends to a closed loop. On this loop the gradient of the objective function is bounded away from zero. We discuss the relevance of these examples to the problem of proving general convergence theorems for minimization algorithms that use search directions.
Springer