The Study On Non-monotonic Trust Region Algorithms For Non-linear Optimization

Trust region method is among most widely adopted methods in solving nonlinear optimization. Because of its good reliability and strong convergence, experts in nonlinear optimization pay close attention to it. In the recent several dozens years, the research about trust region method already is mature, but the fundamental research about non-monotonic trust region algorithm were still imperfect.In the paper, we firstly introduce the elementary knowledge about non- monotonic trust region algorithm the elementary knowledge, including theory, algorithm, application and research situation. We discuss non-monotonic trust region algorithm for unconstrained nonlinear optimization problems in view of Trust Region Model mainly. For detail, we conclude them as follows:1. Summarize the history and historical background and the research present situation about non-monotonic trust region algorithms.2. We separately propose trust region algorithms for unconstrained optimization and linear constrained optimization .and prove them global convergent. Several types about trust region model are given, makes it reasonable. A non-monotonic trust region algorithm is proposed for general constrained optimization, and the convergent result is given.3. A new model which is called as memory model is introduced in solving non-linear optimization which objective function is high dimensional, a non-monotonic trust region algorithm with memory model is proposed for unconstrained optimization, global convergence proof is given for the algorithm, the experiment proves that the algorithm is more effective than other algorithm.