Newton's method for linear inequality systems
نویسنده
چکیده
We describe a modified Newton type algorithm for the solution of linear inequality systems in the sense of minimizing the /, norm of infeasibilities. Finite termination is proved, and numerical results are given.
منابع مشابه
On the Fundamental Role of Interior - PointMethodology
Recently primal-dual interior-point methodology has proven to be an eeective tool in linear programming applications and is now being extended, with great enthusiasm to general nonlinear programming applications. The primary purpose of this current study is to develop and promote the belief that since Newton's method is a tool for square nonlinear systems of equations, the fundamental role of i...
متن کاملNumerical method for solving optimal control problem of the linear differential systems with inequality constraints
In this paper, an efficient method for solving optimal control problems of the linear differential systems with inequality constraint is proposed. By using new adjustment of hat basis functions and their operational matrices of integration, optimal control problem is reduced to an optimization problem. Also, the error analysis of the proposed method is nvestigated and it is proved that the orde...
متن کاملSystem theory for numerical analysis
System theory for numerical analysis has recently become a focus of research. In this paper we regard dynamics of Newton’s method as a nonlinear feedback system and derive convergence conditions, based on the internal model principle and systems of Lur’e type. We then focus our attention on the analysis of the region of absolute stability of Runge-Kutta type methods. We derive a linear matrix i...
متن کاملThe role of linear objective functions in barrier methods
We consider the asymptotic behavior of the Newton/log barrier method for inequality constrained optimization. We show that, when the objective function is linear, an eeective step can be taken along the Newton direction after each reduction in the barrier parameter, leading to eecient performance during the nal stages of the algorithm. This behavior contrasts with the case of a nonlinear object...
متن کاملOn the Newton method for set-valued maps
The Newton method is one of the most powerful tools used to solve systems of nonlinear equations. Its set-valued generalization, considered in this work, allows one to solve also nonlinear equations with geometric constraints and systems of inequalities in a unified manner. The emphasis is given to systems of linear inequalities. The study of the well-posedness of the algorithm and of its conve...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- European Journal of Operational Research
دوره 107 شماره
صفحات -
تاریخ انتشار 1998