In this paper we present the convergence analysis of the inexact infeasible path-following (IIPF) interior point algorithm. In this algorithm the preconditioned conjugate gradient method is used to solve the reduced KKT system (the augmented system). The augmented system is preconditioned by using a block triangular matrix. The KKT system is solved approximately. Therefore, it becomes necessary...

We present new interior regularity criteria for suitable weak solutions of the 3-D Navier-Stokes equations: a suitable weak solution is regular near an interior point z if either the scaled L p,q x,t -norm of the velocity with 3/p + 2/q ≤ 2, 1 ≤ q ≤ ∞, or the L p,q x,t -norm of the vorticity with 3/p + 2/q ≤ 3, 1 ≤ q < ∞, or the L p,q x,t -norm of the gradient of the vorticity with 3/p + 2/q ≤ ...

We present the convergence analysis of the inexact infeasible pathfollowing (IIPF) interior-point algorithm. In this algorithm, the preconditioned conjugate gradient method is used to solve the reduced KKT system (the augmented system). The augmented system is preconditioned by using a block triangular matrix. The KKT system is solved approximately. Therefore, it becomes necessary to study the ...

Biogeochemical properties, including nutrient concentrations, carbon gas fluxes, microbial biomass, and hydrolytic enzyme activities, were determined along a strong nutrient gradient in an ombrotrophic peatland in the Republic of Panama. Total phosphorus in surface peat decreased markedly along a 2.7 km transect from the marginal Raphia taedigera swamp to the interior sawgrass swamp, with simil...

Using the distribution of weak acids to measure the pH gradient (delta pH; interior alkaline) and the distribution of the lipophilic cation [3H]tetraphenylphosphonium+ to monitor the membrane potential (delta psi; interior negative), we studied the electrochemical gradient or protons (delta mu- H+) across the membrane of Micrococcus lysodeikticus cells and plasma membrane vesicles. With reduced...

In this article we consider modiied search directions in the endgame of interior point methods for linear programming. In this stage, the normal equations determining the search directions become ill-conditioned. The modiied search directions are computed by solving perturbed systems in which the systems may be solved ef-ciently by the preconditioned conjugate gradient solver. We prove the conv...

This paper deals with the solution of nonlinear programming problems arising from elliptic control problems by an interior point scheme. At each step of the scheme, we have to solve a large scale symmetric and indefinite system; inner iterative solvers, with adaptive stopping rule, can be used in order to avoid unnecessary inner iterations, especially when the current outer iterate is far from ...

A new Fornberg-like method is presented for computing conformal maps from the interior of the unit disk with m−1 circular holes to the interior of a smooth closed curve with m−1 holes bounded by smooth curves. The method is a Newton-like method for computing the boundary correspondences and the conformal moduli (centers and radii of the circles). The inner linear systems are derived from condit...

Recently Wang, Zheng, Boyd, and Ye [36] proposed a further relaxation of the semidefinite programming (SDP) relaxation of the sensor network localization problem, named edge-based SDP (ESDP). In simulation, the ESDP is solved much faster by interior-point method than SDP relaxation, and the solutions found are comparable or better in approximation accuracy. We study some key properties of the E...