A Descending Dimension Algorithm For The Equality Constrained Multi-objective Programming Problem

In this paper, we have discussed the descending dimension algorithm for multi-objective programming with equality constraints. Also, we have discussed the applications of the optimization method in factual model. We give a new way to research the methods of multi-objective programming in the paper. Firstly, we use the linear weighting method to add the objective functions to a single one. Then, we use the second order form of Taylor expansion to approach the single objective function so that we can get a quadratic program problem. At last, we use the descending dimension form of the K-T condition, which is discovered by professor Li Ze-min, to transform the quadratic program to a system of linear equations. Otherwise, we have discussed the stability of weighted coefficients to the algorithm, compared the method of using the difference method to obtain derivative to the method of using the function expression to get derivative. Else, we have improved the algorithm in the iterative direction, discussed the convergence and proved it under certain conditions. Considering that there are no general algorithms for the multi-objective programming problem, the discussion in this paper give a new way to research it. Moreover a lot of numerical tests have been given for the descending dimension algorithm, comparing with the known algorithms, and the results show satisfying precision, so the algorithm is feasible and effective. Finally, we set up the optimization models for the appraisement problem in the management of scientific research institution and the problem of employment scheme on graduates and solve them, thereinto we solve the latter by both the descending dimension algorithm and the penalty function method, so the application of optimization methods in factual problems are researched in certain deepness.