Primal-dual algorithms, which are proposed to solve reformulated convex-concave saddle point problems, have been proven to be effective for solving a generic class of convex optimization problems, especially when the problems are ill-conditioned. However, the saddle point problem still lacks a distributed optimization framework where primal-dual algorithms can be employed. In this paper, we pro...

The adjoint solution has found many uses in computational simulations where the quantities of interest are the functionals of the solution, including design optimization, error estimation, and control. In those applications where both the solution and the adjoint are desired, the conventional approach is to apply iterative methods to solve the primal and dual problems separately. However, we sh...

We give a simple proof that the RANKING algorithm of Karp, Vazirani and Vazirani [KVV90] is 1-1/e competitive for the online bipartite matching problem. The proof is via a randomized primal-dual argument. Primal-dual algorithms have been successfully used for many online algorithm problems, but the dual constraints are always satisfied deterministically. This is the first instance of a non-triv...

Title of dissertation: PRIMAL-DUAL ALGORITHMS FOR COMBINATORIAL OPTIMIZATION PROBLEMS Julián Mestre Doctor of Philosophy, 2007 Dissertation directed by: Professor Samir Khuller Department of Computer Science Combinatorial optimization problems such as routing, scheduling, covering and packing problems abound in everyday life. At a very high level, a combinatorial optimization problem amounts to...

Title of dissertation: PRIMAL-DUAL ALGORITHMS FOR COMBINATORIAL OPTIMIZATION PROBLEMS Julián Mestre Doctor of Philosophy, 2007 Dissertation directed by: Professor Samir Khuller Department of Computer Science Combinatorial optimization problems such as routing, scheduling, covering and packing problems abound in everyday life. At a very high level, a combinatorial optimization problem amounts to...

We consider a network simplex method using the primal-dual symmetric pivoting rule proposed by Chen, Pardalos, and Saunders. For minimum-cost network-flow problems, we prove global convergence of the algorithm and propose a new scheme in which the algorithm can start from an arbitrary pair of primal and dual feasible spanning trees. For shortest-path problems, we prove the strongly polynomial t...

We discuss a possibility of the extension of a primal-dual interior-point algorithm suggested recently in 1]. We consider optimization problems deened on the intersection of a symmetric cone and an aane subspace. The question of solvability of a linear system arising in the implementation of the primal-dual algorithm is analyzed. A nondegeneracy theory for the considered class of problems is de...

In this lecture, the focus is on primal dual method and its application in designing exact algorithms and approximation algorithms for combinatorial optimization problems. It is a general framework which can solve many problems rather systematically. We first introduce the principles of primal dual program, and then show one example, weighted bipartite matching for designing exact algorithm and...