Based on the relationship between dual variables and sealed-bid Vickrey auction payments (established by Bikhchandani and Ostroy), we consider simpler, specific formulations for various environments. For some of those formulations, we interpret primal-dual algorithms as ascending auctions implementing the Vickrey payments. We focus on three classic optimization problems: assignment, matroid, an...

A dual for linear programming problems with fuzzy parameters is introduced and it is shown that a two person zero sum matrix game with fuzzy pay-o(s is equivalent to a primal–dual pair of such fuzzy linear programming problems. Further certain di6culties with similar studies reported in the literature are discussed. c © 2003 Elsevier B.V. All rights reserved.

The alternating direction method of multipliers (ADM or ADMM) breaks a complex optimization problem into much simpler subproblems. The ADM algorithms are typically short and easy to implement yet exhibit (nearly) state-of-the-art performance for large-scale optimization problems. To apply ADM, we first formulate a given problem into the “ADM-ready” form, so the final algorithm depends on the fo...

In this paper we study a rst-order primal-dual algorithm for convex optimization problems with known saddle-point structure. We prove convergence to a saddle-point with rate O(1/N) in nite dimensions, which is optimal for the complete class of non-smooth problems we are considering in this paper. We further show accelerations of the proposed algorithm to yield optimal rates on easier problems. ...

In this paper, we consider a nonsmooth convex finite-sum problem with conic constraint. To overcome the challenge of projecting onto constraint set and computing full (sub)gradient, introduce primal-dual incremental gradient scheme where only component function two constraints are used to update each sub-iteration in cyclic order. We demonstrate an asymptotic sublinear rate convergence terms su...

Abstract In this paper, we propose a semi-smooth Newton method and primal-dual active set strategy to solve dynamical contact problems with friction. The conditions of Coulomb’s friction can be formulated in the form fixed point problem related quasi-optimization one thanks method. This is based on use (PDAS) strategy. main idea here find correct subset $\mathcal{A}$ <mml:math xmlns:mml="http:/...