Research QP-free Method Based On Linear Equations

Optimal theories and methods have applied to almost every aspect of the real life, such aseconomics, finance, management, engineering, defense, transportation, computers and others.Its aim is to select the best solution from a finite or infinite number of possible types of program-s. With the rapid development of computer, it has great development in many aspects. Later,many authors have studied the optimality conditions of nonlinear programming problems in thefollowing few years, which were represented by the research of H.W.Kuhn and A.W.Tucker. In1960 s and 1970 s, these existed approaches, such as a quasi-Newton method, sequential quadrat-ic programming method and others, had applied to solving real-world problems.With the increasing complexity in the practical issues, it is more and more important andnecessary to find the solutions to these problems. As we all know, sequential quadratic program-ming method is one of the most effective methods for solving nonlinear programming problems.However, in order to assure the global convergence, one or more quadratic programming(QP)subproblems per iteration must be solved. Obviously, the scale of computation of this methodis large. And the search direction obtained is not often feasible. Therefore, it is necessary tostudy some new approaches to avoid these shortcomings.The major work of this paper can be summarized in the following two aspects:(i) Animproved QP-free method which based on linear equations are proposed. The scale of the cal-culation is reduced by our algorithm. And the properties of the descent direction are made fulluse of, moreover the feasibility of the search direction is ensured;(ii) A modified nonmono-tone QP-free method is given, it used the characteristics of nonmonotone techniques, relaxedthe determination condition, and effectively avoid that the algorithm will be stoped at a localminimum.