A constructive global convergence of the mixed barrier-penalty method for mathematical optimization problems

In this paper we develop a generic mixed bi-parametric barrier-penalty method based upon barrier and penalty generic algorithms for constrained nonlinear programming problems. When the feasible set is defined by equality and inequality functional constraints, it is possible to provide an explicit barrier and penalty functions. If such case, the continuity and differentiable properties of the restrictions and objective functions could be inherited to the penalized function. The main contribution of this work is a constructive proof for the global convergence of the sequence generated by the proposed mixed method. The proof uses separately the main results of global convergence of barrier and penalty methods. Finally, for some simple nonlinear problem, we deduce explicitly the mixed barrier–penalty function and illustrate all functions defined in this work. Also we implement MATLAB code for generate iterative points for the mixed method.