Research On Feasibility Monotone And Finitely Convergent Algorithms For Systems Of Nonlinear Inequalities

On one hand, systems of nonlinear inequalities appear largely in practical application fields. On the other hand, the problem is the methods of feasible directions need to be solved. The present results of using the optimization ideas to study the systems of inequalities are mainly systems of linear inequalities or convex systems of nonlinear inequalities. But, the direct and effective methods for solving nonconvex systems of nonlinear inequalities are rare, especially, the methods combining optimization technique.This thesis considers the systems of nonlinear inequalities. And several new algorithms which the initial points are arbitrary are presented. The feasibility of the algorithms are monotonic but not decreasing. The algorithms are ;global convergence and finite termination and the line search is the linear search.The whole thesis is divided int two chapters.Chapter 1, making use of the technique of pivoting operation,the technique of sequential systems of linear equations of studying constrained optimization problems and the idea of strongly subfeasible directions method and , several new algorithms for systems of nonlinear inequalities are presented. The search directions of the algorithms are generated by solving systems of linear equations,which have a unique solution, and by correcting their solutions.Chapter 2, using the technique of (e, d) generalized gradient projection and the idea of strongly subfeasible directions, several new algorithms for systems of nonlinear inequations are presented. The algorithms do not use any pivotal operation,but use the generalized (e, d) - active constraint set to determine the generalized projection matrices. The diagonal matrix of the projection matrix is a new construction method and it is the main function to insure the finite termination.Under suitable assumptions, we analyzed and proved the global convergence and the finite termination of the algorithms. Finally, the algorithms are improved such that they can yield strict interior solutions in a finite number of iterations. This thesis also do many numerical experiments for the given algorithms, and the results show that these algorithms are effective in practical computations.