Some iterative methods for the solution of a symmetric indefinite KKT system
نویسندگان
چکیده
منابع مشابه
Some iterative methods for the solution of a symmetric indefinite KKT system
This paper is concerned with the numerical solution of a Karush–Kuhn– Tucker system. Such symmetric indefinite system arises when we solve a nonlinear programming problem by an Interior–Point (IP) approach. In this framework, we discuss the effectiveness of two inner iterative solvers: the method of multipliers and the preconditioned conjugate gradient method. We discuss the implementation deta...
متن کاملSome Generalizations and Modifications of Iterative Methods for Solving Large Sparse Symmetric Indefinite Linear Systems
and Applied Analysis 3 Instead of solving for y directly from the triangular linear system (15), Paige and Saunders [1] factorize the matrix Tn into a lower triangular matrix with bandwidth three (resulting in the SYMMLQmethod). Also, we have TnQn−1 = ̂ Ln = [ [ [ [ [ [ [ [ [ [ γ0 δ1 γ1 ε2 δ2 γ2 d d d εn−3 δn−3 γn−3 εn−2 δn−2 γn−2 εn−1 δn−1 γn−1 ] ] ] ] ] ] ] ] ]
متن کاملSymplectic and symmetric methods for the numerical solution of some mathematical models of celestial objects
In the last years, the theory of numerical methods for system of non-stiff and stiff ordinary differential equations has reached a certain maturity. So, there are many excellent codes which are based on Runge–Kutta methods, linear multistep methods, Obreshkov methods, hybrid methods or general linear methods. Although these methods have good accuracy and desirable stability properties such as A...
متن کاملNewton-KKT interior-point methods for indefinite quadratic programming
Two interior-point algorithms are proposed and analyzed, for the (local) solution of (possibly) indefinite quadratic programming problems. They are of the Newton-KKT variety in that (much like in the case of primal-dual algorithms for linear programming) search directions for the “primal” variables and the Karush-Kuhn-Tucker (KKT) multiplier estimates are components of the Newton (or quasi-Newt...
متن کاملPreconditioning and iterative solution of symmetric indefinite linear systems arising from interior point methods for linear programming
We propose to compute the search direction at each interior-point iteration for a linear program via a reduced augmented system that typically has a much smaller dimension than the original augmented system. This reduced system is potentially less susceptible to the ill-conditioning effect of the elements in the (1, 1) block of the augmented matrix. A preconditioner is then designed by approxim...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Computational Optimization and Applications
سال: 2007
ISSN: 0926-6003,1573-2894
DOI: 10.1007/s10589-007-9039-7