Many separable dynamic incentive problems have primal recursive formulations in which utility promises serve as state variables. We associate families of dual recursive problems with these by selectively dualizing constraints. We make transparent the connections between recursive primal and dual approaches, relate value iteration under each and give conditions for such value iteration to be con...

Computational methods are proposed for solving a convex quadratic program (QP). Active-set methods are defined for a particular primal and dual formulation of a QP with general equality constraints and simple lower bounds on the variables. In the first part of the paper, two methods are proposed, one primal and one dual. These methods generate a sequence of iterates that are feasible with respe...

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...

In this paper we propose and analyze two dual methods based on inexact gradient information and averaging that generate approximate primal solutions for smooth convex optimization problems. The complicating constraints are moved into the cost using the Lagrange multipliers. The dual problem is solved by inexact first order methods based on approximate gradients and we prove sublinear rate of co...

We address the question of whether the primal-dual approach for the design and analysis of online algorithms can be applied to nonmonotone problems. We provide a positive answer by presenting a primal-dual analysis to the online algorithm of Awerbuch et al. [AAPW01] for routing virtual circuits with unknown durations.

We show that if there exists a strongly polynomial time algorithm that nds a basis which is optimal for both the primal and the dual problems given an optimal solution for one of the problems then there exists a strongly polyno mial algorithm for the general linear programming problem On other hand we give a strongly polynomial time algorithm that nds such a basis given any pair of optimal solu...