IN THIS PAPER, WE PROPOSE A NEWTON-TYPE ALGORITHM FOR NONCONVEX MULTIOBJECTIVE Optimization PROBLEMS. THE PRESENTED TERMINATES, WHEN THE TERMINATION CONDITIONS ARE SATISFIED. CONVERGENCE OF THE ALGORITHM IS CONSIDERED.

IN THIS PAPER, WE ARE GOING TO PROPOSE A GLOBAL INTERACTIVE ALGORITHM ENABLING THE DECISION MAKER (DM) TO APPLY FREELY SEVERAL CONVENIENT METHODS WHICH BEST FIT HIS/HER PREFERENCES. TO THIS END, A GENERAL SCALARIZING PROBLEM FOR Multi-Objective PROGRAMMING IS SUGGESTED AND THE RELATION BETWEEN OPTIMAL SOLUTIONS OF THE INTRODUCED SCALARIZED PROBLEM AND (WEAKLY, PROPERLY) EFFICIENT SOLUTIONS OF THE MAIN Multi-Objective Optimization PROBLEM (MOP) IS DISCUSSED. UTILIZING THE PROPOSED SCALARIZED PROBLEM, WE SUGGEST AN INTERACTIVE METHOD THAT ENABLES THE DM TO SPECIFY HIS/HER PREFERENCES IN DIFFERENT WAYS WITH CAPABILITY TO CHANGE HIS/HER PREFERENCES ANYTIME DURING THE ITERATIONS OF THE ALGORITHM.

THE OBJECTIVE OF THIS PAPER IS TO FIND A METHOD FOR FINDING THE WEAKLY EFFICIENT POINTS OF A LINEAR MULTIOBJECTIVE Optimization PROBLEM IN RN. IF THERE EXISTS TWO OBJECTIVE FUNCTIONS IN THE Multi-Objective Optimization PROBLEM, SINCE THE OBJECTIVE FUNCTIONS THE PROBLEM ARE LINEAR, THE WEAKLY EFFICIENT POINTS OF THIS PROBLEM ARE EASILY FOUND. BY USE OF THE WEAKLY EFFICIENT POINTS OF TWO FUNCTIONS IN THE MULTIOBJECTIVE Optimization PROBLEM, WE OBTAIN THE WEAKLY EFFICIENT POINTS OF THE MAIN PROBLEM. AT THE END THE PROPOSED METHOD IS CODED BY MATLAB LANGUAGE AND EVALUATED FOR SOME EXAMPLES.