A note on using alternative second-order models for the subproblems arising in barrier function methods for minimization
For an inequality constrained minimization problem a weighted/shifted logarithmic barrier function method is presented. Since in the inner iteration the use of the standard Newton method has a number of potential dangers (the Newton step may not be possible, badly conditioned Newton equation, etc.), the authors recommend in \((k + 1)\)th iteration to determine a stationary point of the barrier function. The main attention of the paper is devoted to the relationship between the shifts and weights for one inner iteration and for the next and its implication for the case of solving successive inner iteration subproblems.
scientific article; zbMATH DE number 691557