Trust-region Algorithm For Nonlinear Programming

The nonlinear optimization is developed in the 1950s. It discussed the best choice of the nonlinear programming problem, and made the calculation method of the best solution. For the development and application of electronic computers, nonlinear optimization theory and method made a greate development. And now, it had become an important branch of the operations, and in science, engineering technology, economic management, especially the optimization design. It had become a very active discipline.. Trust region method is a kind of new method, this method and line search are the two main kinds of method for solving nonlinear programming. Trust region algorithm request the distance between the new iteration and current iteration does not exceed a certain quantity of control in each iteration. Therefore,the selection of appropriate trust region method to solve the nonlinear programming problem is worthy research.In this paper, we discuss the two aspects:1 A nonmonotone adaptive–BFGS trust-region method for unconstrained potimiza- tion is presented. The trust-region radius in this method is automatically determined by using first order information. At the same time we use the advantage of the BFGS algorithm. Under certain conditions, the global and superlinear convergence of the algo- rithm are proved.2 A adaptive–BFGS trust-region method for linear constrained potimization is po- sed. The trust-region radius in this method is automatically detemined with first order information, At the same time we use the advatage of the BFGS algorithm. Under cer- tain conditions, the global conertgence of the algorithm is proved.