Lagrangean dualization and subgradient optimization techniques are frequently used within the field of computational optimization for finding approximate solutions to large, structured optimization problems. The dual subgradient scheme does not automatically produce primal feasible solutions; there is an abundance of techniques for computing such solutions (via penalty functions, tangential app...

Interior-point methods possess strong theoretical properties and have been successfully applied to a wide variety of linear and nonlinear programming applications. This paper presents a class of algorithms, based on interior-point methodology, for performing regularized maximum likelihood reconstructions on 3-D emission tomography data. The algorithms solve a sequence of subproblems that conver...

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...

This paper analyzes sequences generated by infeasible interior point methods. In convex and nonconvex settings, we prove that moving the primal feasibility at the same rate as complementarity will ensure that the Lagrange multiplier sequence will remain bounded, provided the limit point of the primal sequence has a Lagrange multiplier, without constraint qualification assumptions. We also show ...

Primal–dual interior point methods and the HKM method in particular have been implemented in a number of software packages for semidefinite programming. These methods have performed well in practice on small to medium sized SDP’s. However, primal–dual codes have had some trouble in solving larger problems because of the storage requirements and required computational effort. In this paper we de...

Many theories suggest that a threatening situation impacts health because it affects core needs. Our assumption was that a set of interdependent ;perceived primal threats' to basic human needs (self-preservation, social integration, personal identity and growth, and positive worldview), which result from the presence of a disease, are related to illness perceptions and subjective health. Partic...

There is a natural graph associated to the zero-divisors of a commutative semiring with non-zero identity. In this article we essentially study zero-divisor graphs with respect to primal and non-primal ideals of a commutative semiring R and investigate the interplay between the semiring-theoretic properties of R and the graph-theoretic properties of ΓI(R) for some ideal I of R. We also show tha...

In a multiperiod dynamic network flow problem, we model uncertain arc capacities using scenario aggregation. This model is so large that it may be difficult to obtain optimal integer or even continuous solutions. We develop a Lagrangian decomposition method based on the structure recently introduced in [9]. Our algorithm produces a near-optimal primal integral solution and an optimum solution t...

Gurevich and Neeman introduced Distributed Knowledge Authorization Language (DKAL). The world of DKAL consists of communicating principals computing their own knowledge in their own states. DKAL is based on a new logic of information, the so-called infon logic, and its efficient subsystem called primal logic. In this paper we simplify Kripkean semantics of primal logic and study various extensi...

This paper describes efficient algorithms for determining how buffer space should be allocated in a flow line. We analyze two problems: a primal problem, which minimizes total buffer space subject to a production rate constraint; and a dual problem, which maximizes production rate subject to a total buffer space constraint. The dual problem is solved by means of a gradient method, and the prima...