A Logarithmic Barrier Approach to Fischer Function

Recently, reformulation of variational inequalities and complementarity problems as a system of equations or an optimization problem has become a hot topic in the eld of mathematical programming. Various merit functions play important roles in such reformulations. In this paper, among others, we consider the well-known Fischer function and explore its relationship with other merit functions. It is shown that the Fischer function can be derived from a logarithmic barrier penalty method for constrained minimization. Based on the logarithmic barrier approach, some new merit functions are given and their properties are explored.