Solving linear systems involved in constrained optimization

Singular constrained linear systems

In the linear system Ax = b the points x are sometimes constrained to lie in a given subspace S of column space of A. Drazin inverse for any singular or nonsingular matrix, exist and is unique. In this paper, the singular consistent or inconsistent constrained linear systems are introduced and the effect of Drazin inverse in solving such systems is investigated. Constrained linear system arise ...

singular constrained linear systems

in the linear system ax = b the points x are sometimes constrained to lie in a given subspace s of column space of a. drazin inverse for any singular or nonsingular matrix, exist and is unique. in this paper, the singular consistent or inconsistent constrained linear systems are introduced and the effect of drazin inverse in solving such systems is investigated. constrained linear system arise ...

Optimization of linear systems of constrained configurationt

Optimization of linear systems of constrained configuration

There exists a well-developed theory for the optimal regulation of a linear system [1]. The optimal controller incorporates feedbacks from every state variable. It thus generates the control signal from the minimum amount of information necessary to predict the motion of the system. If some of the state variables cannot be measured they may be reconstructed from the available measurements by an...

A New Hyperplane Method for Solving Linear Inequality Constrained Optimization ⋆

For solving linear inequality constrained optimization, a new hyperplane method is introduced. The trust region approach for unconstraint optimization is used to minimize objective function on the hyperplane defined by the current iterative point. If a separate indicator shows that it is not worthwhile to find a better point in the current hyperplane. Then a line search along a chopped directio...