ABSTRACT
Discusses one of the interior-point methods, the potential deduction method. There are two classes of potential-reduction algorithms, the primal potential-reduction algorithms and primal-dual potential-reduction algorithms. Both types algorithms use logarithmic barrier functions as the objective functions. But the potential functions used primal-dual potential logarithmic barrier functions have a more balanced consideration on both primal and dual variables, they are now considered better than their counterparts. Therefore, this chapter discusses a potential-reduction algorithm that uses a logarithmic barrier function involving both primal and dual variables. It is pointed out that the primal-dual potential-reduction interior-point algorithms are not as efficient as primal-dual path-following interior-point algorithms. However, potential-reduction interior-point method has found to be useful in the development of interior-point algorithms for nonlinear programming. This is the main reason that it is included in this chapter.
