Let G be an abelian group and let R be a commutative G-graded super-ring (briefly, graded super-ring) with unity 1 6= 0. We say that a ∈ h(R), where h(R) is the set of homogeneous elements in R, is weakly prime to a graded superideal I of R if 0 6= r a ∈ I , where r ∈ h(R), then r ∈ I . If ν(I ) is the set of homogeneous elements in R that are not weakly prime to I , then we define I to be weak...

We propose a generic path-following scheme which is essentially a method of centers that can be implemented with a variety of algorithms. The complexity estimate is computed on the sole assumption that a certain local quadratic convergence property holds, independently of the speciic algorithmic procedure in use, primal, dual or primal-dual. We show convergence in O(p n) iterations. We verify t...

This paper presents estimates of the degree of returns to scale using nonparametric measures of primal and dual productivity for 2-digit US manufacturing industries. As part of the analysis, the cyclical behaviour of primal and dual productivity measures are considered, time-varying markups are allowed for, and the small sample properties of the instrumental variables estimator used to derive t...

Primal infon logic (PIL) was introduced in 2009 in the framework of policy and trust management. In the meantime, some generalizations appeared, and there have been some changes in the syntax of the basic PIL. This paper is on the basic PIL, and one of our purposes is to “institutionalize” the changes. We prove a small-model theorem for the propositional fragment of basic primal infon logic (PP...

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...