The Primal-dual Interior Point Algorithm For Nonlinear Programming

The nonlinear programming source the production process arrangement,the optimal design of the process,the quality control,inventory control,system automation con-trol,management science,forecasting and many other areas,under the increasingly closely development with various areas,the optimal theory and the algorithm of the nonlinear programming get much more concern.Since 1984,Karmarkar firstly present-ed the interior point algorithm for solving the optimization problem,more primal-dual interior point algorithm came out to make it become one of the most efficient method for nonlinear programming problems.The key of this method is to construct a kind of merit function in order to find the descent direction.Firstly,we summary primal-dual interior algorithm of nonlinear programming.Nextly,we present a new primal-dual in-terior method for solving nonlinear programming problems.Finally,we give the proof of convergence of this method as well as the examples of particular value under the algorithm.The choice of the initial point plays an important role in the computation efficiency of the primal-dual interior algorithm,but most of the algorithms are currently set the initial point within feasible region.While feasible region is much more complex,it is difficult to find the initial plint in the feasible region.Thus it is necessary to expand the sclection scope of the initial point,in order to improve the efficiency of the algo-rithm Based on above reasons,we apply a perturbation technique to the constrained fuunctions and present a new primal-dual interior point method for solving nonlinear programming problems.When the perturbation parameters is 1,we can get the new feasible region much larger than the original feasible region;while the perturbation pa-raineters is 0,the expanded feasible region convergence in the origin region.Furthermore two examples show the effectiveness of the algorithm.