It has been recently claimed that the most-obtuse-angle pivot rule is one of the best choices for Phase I linear programs based on the simplex method. In this short note we give two instances of Phase I cycling under such ratio-test-free rule, both when it is used to obtain primal feasibility and when trying to achieve dual feasibility with its unnormalized counterpart. A crash procedure that i...

We represent the Ising model of statistical physics by Forney factor graphs in the primal and in the dual domains. By analogy with Kirchhoff’s voltage and current laws, we show that in the primal Forney factor graph, the dependency among the variables is along the cycles, whereas in the dual Forney factor graph, the dependency is on the cutsets. In the primal (resp. dual) domain, dependent vari...

In this paper, we consider a general primal-dual nonlinear rescaling (PDNR) method for convex optimization with inequality constraints. We prove the global convergence of the PDNR method and estimate the error bounds for the primal and dual sequences. In particular, we prove that, under the standard second-order optimality conditions, the error bounds for the primal and dual sequences converge ...

A primal-dual active set method for quadratic problems with bound constraints is presented which extends the infeasible active set approach of Kunisch and Rendl [17]. Based on a guess of the active set, a primal-dual pair (x,α) is computed that satisfies stationarity and the complementary condition. If x is not feasible, the variables connected to the infeasibilities are added to the active set...

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...

The paper considers a current example of Wächter and Biegler which is shown not to converge for the standard primal-dual interior-point method for nonlinear programming. Three possible solutions to the problem are derived and discussed, including shifting slack variables, a trust region method, and a modified barrier method. The paper then compares LOQO, a line-search interior-point code, with ...

Nanobacteria or living nanovesicles are of great interest to the scientific community because of their dual nature: on the one hand, they appear as primal biosystems originating life; on the other hand, they can cause severe diseases. Their survival as well as their pathogenic potential is apparently linked to a self-synthesized protein-based slime, rich in calcium and phosphate (when available...

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...