We propose two approximate versions of the first-order primal-dual algorithm (PDA) to solve a class convex-concave saddle point problems. The introduced criteria are easy implement in sense that they only involve subgradient certain function at current iterate. first PDA solves both subproblems inexactly and adopts absolute error criteria, which based on non-negative summable sequences. Assumin...

23] C.L. Monma and A.J. Morton. Computational experimental with a dual aane variant of Karmarkar's method for linear programming. extension of Karmarkar type algorithm to a class of convex separable programming problems with global linear rate of convergence. Techni-28] J. Renegar. A polynomial-time algorithm based on Newton's method for linear programming. Implementing an interior point method...

We analyze a primal-dual pair of problems generated via a duality theory introduced by Svaiter. We propose a general algorithm and study its convergence properties. The focus is a general primal-dual principle for strong convergence of some classes of algorithms. In particular, we give a different viewpoint for the weak-to-strong principle of Bauschke and Combettes and unify many results concer...

A new primal-dual algorithm is presented for solving a class of non-convex minimization problems. This algorithm is based on canonical duality theory such that the original non-convex minimization problem is first reformulated as a convex-concave saddle point optimization problem, which is then solved by a quadratically perturbed primal-dual method. Numerical examples are illustrated. Comparing...

We consider the problem of minimizing the sum of a strongly convex function and a term comprising the sum of extended real-valued proper closed convex functions. We derive the primal representation of dual-based block descentmethods and establish a relation between primal and dual rates of convergence, allowing to compute the efficiency estimates of different methods. We illustrate the effectiv...

We discuss an adaptation of the famous primal-dual 1matching algorithm to balanced network flows which can be viewed as a network flow description of capacitated matching problems. This method is endowed with a sophisticated start-up procedure which eventually makes the algorithm strongly polynomial. We apply the primal-dual algorithm to the shortest valid path problem with arbitrary arc length...

We establish connections between the facial reduction algorithm of Borwein and Wolkowicz and the self-dual homogeneous model of Goldman and Tucker when applied to conic optimization problems. Specifically, we show the self-dual homogeneous model returns facial reduction certificates when it fails to return a primal-dual optimal solution or a certificate of infeasibility. Using this observation,...

This paper investigates the communication complexity of distributed resource allocation problems. Communication complexity, which has emerged from computer science, measures the minimal number of communicated bits needed to solve some classes of problems regardless of the used algorithm, when the communication is lossless. We introduce two complexity measures for finding primal/dual saddle poin...

Network utility maximization problems arise when the design of a data network is formulated as a whole by means of utility functions. Although fully centralized algorithms are theoretically possible, in practical networks it is desirable to obtain distributed algorithms of simple implementation. In the existing literature, this is typically achieved by means of the so-called dual decomposition ...

We analyze a primal-dual pair of problems generated via a duality theory introduced by Svaiter. We propose a general algorithm and study its convergence properties. The focus is a general primal-dual principle for strong convergence of some classes of algorithms. In particular, we give a different viewpoint for the weak-to-strong principle of Bauschke and Combettes and unify many results concer...