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...

We study primal solutions obtained as a by-product of subgradient methods when solving the Lagrangian dual of a primal convex constrained optimization problem (possibly nonsmooth). The existing literature on the use of subgradient methods for generating primal optimal solutions is limited to the methods producing such solutions only asymptotically (i.e., in the limit as the number of subgradien...

In this paper we introduce a primal-dual affine scaling method. The method uses a searchdirection obtained by minimizing the duality gap over a linearly transformed conic section. This direction neither coincides with known primal-dual affine scaling directions [12, 21], nor does it fit in the generic primal-dual method [15]. The new method requires O(√nL) main iterations. It is shown that the ...

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...

Regularized empirical risk minimization problems are fundamental tasks in machine learning and data analysis. Many successful approaches for solving these problems are based on a dual formulation, which often admits more efficient algorithms. Often, though, the primal solution is needed. In the case of regularized empirical risk minimization, there is a convenient formula for reconstructing an ...

In this paper, we show that the moving directions of the primal-affine scaling method (with logarithmic barrier function), the dual-affine scaling method (with logarithmic barrier function), and the primal-dual interior point method are merely the Newton directions along three different algebraic "paths" that lead to a solution of the Karush-Kuhn-Tucker conditions of a given linear programming ...

surfaces of order t, the image of C2s-i for a particular surface is a conical curve of order (25 — 1)/. In Sr, the image of any point on the base Msi or Mt2 is a conic. The lines joining points of M to a particular point of/ i form a conical primal with a point vertex. I t is met by the corresponding primal of the second pencil in a manifold M\^-2)t or M\2^-i)t according as there is contact or ...

Universum-support vector machine (U-SVM) is an elegant method for 2-class classification problem. It is systematically studied in this paper, including the existence and uniqueness of the primal problem as well as the relation between the solutions of primal problem and dual problem. We find that U-SVM uses 3-class classification approach to solve the 2-class classification problem. So we have ...

The primal-dual method increases the dual variables gradually until some dual constraint becomes tight. Then, the primal variable corresponding to the tight dual constraint is ‘bought’ (or selected), and the process continues till we get a feasible primal solution. Next, we compare the value of the primal solution to the value of the dual solution to get an appropriate approximation factor (or ...

As is well known, Q-superlinear or Q-quadratic convergence of the primal-dual sequence generated by an optimization algorithm does not, in general, imply Q-superlinear convergence of the primal part. Primal convergence, however, is often of particular interest. For the sequential quadratic programming (SQP) algorithm, local primal-dual quadratic convergence can be established under the assumpti...