A Primal-Dual Interior-Point FS Algorithm And Its Global Convergence

Penalty-free-type methods, such as filter methods, have become one of hot spots in the field of nonlinear programming. A great number of numerical experiments have shown their impressing efficiency of filter methods.Interior point methods(IPMs) are one of the most important classes of algorithms in nonlinear programming.They are now being generalized to nonlinear programming and have been applied into many fields such as fiance and power system. Of all the iterior point methods,primal dual interior point methods(PDIPMs) are considered as the most successful ones.FS method is a new penalty-free-type method.This class of algorithms sets a FS value to control the degree of feasibility violation of trial points and uses some techniques to reduce the value of objective function.In this paper, we present an algorithm that combines the ideas of FS technique and interior point framework. The new algorithm has no any choice of penalty parameter and penalty function, and it does not use the filter technique either.We analyze the global convergence of the main algorithm under appropriate assumptions.The preliminary numerical results are reported.