The paper is a simplified exposition of an early combined phase I-phase II method for linear programming. The method works from an infeasible start. Besides, there is no need for regularity conditions if the method is applied to a primal-dual formulation.

We consider semilinear elliptic equations ∆u ± ρ(x)f(u) = 0, or more generally ∆u + φ(x, u) = 0, posed in RN (N ≥ 3). We prove that the existence of bounded positive entire solutions is closely related to the existence of bounded solution for ∆u + ρ(x) = 0 in RN . Many sufficient conditions which are invariant under the isometry group of RN are established. Our proofs use the standard barrier m...

3. page 13, lines 12–13: Insert a phrase to stress that we consider only monotone LCP in this book, though the qualifier ”monotone” is often omitted. Replace the sentence preceding the formula (1.21) by The monotone LCP—the qualifier ”monotone” is implicit throughout this book—is the problem of finding vectors x and s in I R that satisfy the following conditions: 4. page 13, line −12: delete “o...

We formulated a discrete time model in order to study optimal control strategies for single influenza outbreak. In our model, we divided the population into four classes: susceptible, infectious, treated, and recovered individuals. The total population was divided into subgroups according to activity or susceptibility levels. The goal was to determine how treatment doses should be distributed i...

In this paper we present a primal-dual interior-point algorithm to solve a class of multi-objective network flow problems. More precisely, our algorithm is an extension of the single-objective primal infeasible dual feasible inexact interior point method for multi-objective linear network flow problems. Our algorithm is contrasted with standard interior point methods and experimental results on...

This paper presents a methodology for the classification of power system voltage stability, the trajectory of which to instability is monotonic, using an interior point method based support vector machine (IPMSVM). The SVM based voltage stability classifier can provide real-time stability identification only using the local measurement data, without the topological information conventionally used.

We formulate a discrete time model to identify and evaluate the role of optimal control strategies on influenza transmission. We divide the population in two subgroups defined according to the contact activity or susceptibility levels. The individuals are identified as susceptible, infectious, treated, and recovered. The potential effect of antiviral treatment considering unlimited and limited ...

A new IPM (Interior Point Method) for LPs has been discussed in [9, 10] based on a centering step that attempts to maximize the radius of the inscribed sphere with center on the current objective plane, and using descent directions derived without using matrix inversions. The method is a descent method and may be called the sphere method for LP. In contrast to all the existing IPMs which involv...