In this paper we propose an efficient distributed algorithm for solving loosely coupled convex optimization problems. The algorithm is based on a primal-dual interior-point method in which we use the alternating direction method of multipliers (ADMM) to compute the primal-dual directions at each iteration of the method. This enables us to join the exceptional convergence properties of primal-du...

Motivated by practical numerical issues in a number of modeling and simulation problems, we introduce the notion of a compatible dual complex to a primal triangulation, such that a simplicial mesh and its compatible dual complex (made out of convex cells) form what we call a primal-dual triangulation. Using algebraic and computational geometry results, we show that compatible dual complexes exi...

We consider empirical risk minimization of linear predictors with convex loss functions. Such problems can be reformulated as convex-concave saddle point problems, and thus are well suitable for primal-dual first-order algorithms. However, primal-dual algorithms often require explicit strongly convex regularization in order to obtain fast linear convergence, and the required dual proximal mappi...

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...

Based on optimal theory, Kelly model realizes the bandwidth allocation on network with proportional fairness and has asymptotical stability. However, the primal algorithm of Kelly model leads to the packet accumulation in the queue of the bottleneck link. By using heuristic fuzzy rules, this paper designs a fuzzy controller to adjust the additive increase parameter of the primal algorithm dynam...

Primal-dual algorithms have played an integral role in recent developments in approximation algorithms, and yet there has been little work on these algorithms in the context of LP relaxations that have been strengthened by the addition of more sophisticated valid inequalities. We introduce primal-dual schema based on the LP relaxations devised by Carr, Fleischer, Leung & Phillips for the minimu...

A FETI-DP formulation for three dimensional elasticity problems on non-matching grids is considered. To resolve the nonconformity of the finite elements, a mortar matching condition is imposed on subdomain interfaces. The mortar matching condition are considered as weak continuity constraints in the FETIDP formulation. A relatively large set of primal constraints, which include average and mome...

We represent the Ising model of statistical physics by Forney factor graphs in the primal and in the dual domains. By analogy with Kirchhoff’s voltage and current laws, we show that in the primal Forney factor graph, the dependency among the variables is along the cycles, whereas in the dual Forney factor graph, the dependency is on the cutsets. In the primal (resp. dual) domain, dependent vari...

In this paper, we consider a general primal-dual nonlinear rescaling (PDNR) method for convex optimization with inequality constraints. We prove the global convergence of the PDNR method and estimate the error bounds for the primal and dual sequences. In particular, we prove that, under the standard second-order optimality conditions, the error bounds for the primal and dual sequences converge ...

A primal-dual active set method for quadratic problems with bound constraints is presented which extends the infeasible active set approach of Kunisch and Rendl [17]. Based on a guess of the active set, a primal-dual pair (x,α) is computed that satisfies stationarity and the complementary condition. If x is not feasible, the variables connected to the infeasibilities are added to the active set...