Primal–dual interior point methods and the HKM method in particular have been implemented in a number of software packages for semidefinite programming. These methods have performed well in practice on small to medium sized SDP’s. However, primal–dual codes have had some trouble in solving larger problems because of the storage requirements and required computational effort. In this paper we de...

In this paper we consider a linear programming problem with the underlying matrix unimodular, and the other data integer. Given arbitrary near optimum feasible solutions to the primal and the dual problems, we obtain conditions under which statements can be made about the value of certain variables in optimal vertices. Such results have applications to the problem of determining the stopping cr...

This paper proposes two sets of rules Rule G and Rule P for controlling step lengths in a generic primal dual interior point method for solving the linear program ming problem in standard form and its dual Theoretically Rule G ensures the global convergence while Rule P which is a special case of Rule G ensures the O nL iteration polynomial time computational complexity Both rules depend only o...

We present a quadratic Discrete-time Optimal Control problem generator, written in C, with options for Degeneracy, Activity and Conditioning (DOCDAC). We use the generator to investigate badly conditioned and degenerate extended linear-quadratic problems (ELQPs) by solving such problems with primal-dual projected gradient and interior-point methods. The benefit of using second-order information...

Our original results refer to dualistic structure on primaldual interior-point methods for symmetric cone programs with linear constraints. It is shown that scalings by the Nesterov-Todd direction are generated by middle points of geodesics joining with primal interior points and dual interior points. Finally we relate power classes of search directions with geodesics and weighted geometric mea...

We propose a polynomial time primal dual potential reduction algorithm for linear pro gramming The algorithm generates sequences d and v rather than a primal dual interior point xk sk where di q xi s k i and v k i q xi s k i for i n Only one element of d is changed in each iteration so that the work per iteration is bounded by O mn us ing rank one updating techniques The usual primal dual itera...