Numerical Experiments with Methods for Solving the KKT Equations
نویسندگان
چکیده
In many seqential quadratic programming algorithms for constrained optimization the calculation of an effective search direction depends on the (estimated) Hessian of the Lagrangian being positive definite on the null space of the active constraints. This paper reports some numerical experience with two techniques for checking the properties of the Hessian and, if necessary, modifying it during the solution of the KKT equations.
منابع مشابه
Numerical solution of KKT systems in PDE-constrained optimization problems via the affine scaling trust-region approach
A recently proposed trust-region approach for bound-constrained nonlinear equations is applied to the KKT systems arising from the discretization of a class of PDE-constrained optimization problems. Two different implementations are developed that take into account the large dimension and the special structure of the problems. The linear algebra phase is analyzed considering the possibility of ...
متن کاملOn Efficiency of Non-Monotone Adaptive Trust Region and Scaled Trust Region Methods in Solving Nonlinear Systems of Equations
In this paper we run two important methods for solving some well-known problems and make a comparison on their performance and efficiency in solving nonlinear systems of equations. One of these methods is a non-monotone adaptive trust region strategy and another one is a scaled trust region approach. Each of methods showed fast convergence in special problems and slow convergence in other o...
متن کاملStable Reduction to Kkt Systems in Barrier Methods for Linear and Quadratic Programming
We discuss methods for solving the key linear equations within primal-dual barrier methods for linear and quadratic programming. Following Freund and Jarre, we explore methods for reducing the Newton equations to 2× 2 block systems (KKT systems) in a stable manner. Some methods require partitioning the variables into two or more parts, but a simpler approach is derived and recommended. To justi...
متن کاملA new approach for solving the first-order linear matrix differential equations
Abstract. The main contribution of the current paper is to propose a new effective numerical method for solving the first-order linear matrix differential equations. Properties of the Legendre basis operational matrix of integration together with a collocation method are applied to reduce the problem to a coupled linear matrix equations. Afterwards, an iterative algorithm is examined for solvin...
متن کاملGGMRES: A GMRES--type algorithm for solving singular linear equations with index one
In this paper, an algorithm based on the Drazin generalized conjugate residual (DGMRES) algorithm is proposed for computing the group-inverse solution of singular linear equations with index one. Numerical experiments show that the resulting group-inverse solution is reasonably accurate and its computation time is significantly less than that of group-inverse solution obtained by the DGMRES alg...
متن کامل