An interior point method (IPM) defines a search direction at each interior point of a region. These search directions form a direction field which in turn gives rise to a system of ordinary differential equations (ODEs). The solutions of the system of ODEs can be viewed as underlying paths in the interior of the region. In [C.-K. Sim and G. Zhao, Math. Program. Ser. A, 110 (2007), pp. 475–499],...

We study an initial-boundary value problem for a singularly perturbed reaction–convection–diffusion system. Asymptotic analysis is used to construct a domain decomposition method for the system to describe the asymptotic nature of the interactions between the boundary layers, interior layers and shock layers. Our results show that the formation of boundary layers and shock layers depends upon i...

For all M,N∈P(U) such that M⊂N, we first introduced the definitions of (M,N)-uni-soft ideals and (M,N)-uni-soft interior ideals of an ordered semigroup and studied them. When M=∅ and N=U, we meet the ordinary soft ones. Then we proved that in regular and in intra-regular ordered semigroups the concept of (M,N)-uni-soft ideals and the (M,N)-uni-soft interior ideals coincide. Finally, we introduc...

Estimation of nonlinear dynamic models from data poses many challenges, including model instability and non-convexity of long-term simulation fidelity. Recently Lagrangian relaxation has been proposed as a method to approximate simulation fidelity and guarantee stability via semidefinite programming (SDP), however the resulting SDPs have large dimension, limiting their utility in practical prob...

(Rece;"cd 00 Monlh 20Ox; final ...,rsiaH recei"ed 00 Monlh £OOX) In this paper a primal-dual interior-point algorithm for semidefinite programming that can be used for analrzing e.g_ polytopic linear difleTential indusions is tailored in order to be more computationally efficient. The key to th" speedup is to allow for inexact ..,,,rch directions in the inteciOT_point algorithm. Th.,..., are ob...

OBJECTIVE This work aims to perform a biomechanical test to evaluate the effect of interior supporting system and tantalum rod in simulating the treatment of ischemic necrosis of the femoral head. METHOD Three models were established: control group (group A), interior supporting system group (group B), and tantalum rod group (group C). Step-by-step loading was applied on the top of the femora...

Creating as-built plans of building interiors is a challenging task. In this paper we present a semi-automatic modelling system for creating residential building interior plans and their integration with existing map data to produce building models. Taking a set of imprecise measurements made with an interactive mobile phone room mapping application, the system performs spatial adjustments in a...

A topology optimization based approach is proposed to study the optimal configuration of stiffeners for the interior sound reduction. Since our design target is aimed at reducing the low frequency noise, a coupled acoustic-structural conservative system without damping effect is considered. Modal analysis method is used to evaluate the interior sound level for this coupled system. To formulate ...

Some implementations of interior-point algorithms obtain their search directions by solving symmetric indeenite systems of linear equations. The conditioning of the coeecient matrices in these so-called augmentedsystems deteriorateson later iterations, as some of the diagonal elements grow without bound. Despite this apparent diiculty, the steps produced by standard factorization procedures are...