next up previous

2.2.3 Convergence Criteria

The simplest test for optimality of each in the basic local minimizer algorithm 2.1 involves the following gradient condition:

The parameter is a small positive number such as square root of machine precision, ( is the smallest number such that the floating point value of is greater than the floating representation of 1). For large-scale problems, the Euclidean norm divided by , or the max norm, , may be used to replace or in the left side of equation (26). This measures instead an average gradient element.