A common objective in many applied problems is to infer properties of the interior of an object based on tomographic (line-integral) projections. In a number of applications the ultimate goal is to characterize (e.g., detect, locate) regions of the interior which are, in some sense, anomalous. A major challenge is to develop methods which can characterize anomalies directly in the data domain (...

We consider the Riemannian geometry defined on a convex set by the Hessian of a selfconcordant barrier function, and its associated geodesic curves. These provide guidance for the construction of efficient interior-point methods for optimizing a linear function over the intersection of the set with an affine manifold. We show that algorithms that follow the primal-dual central path are in some ...

In view of providing an explicit representation of the convex hull by listing all the facets, it is interesting to describe the integral feasible region in terms of interior points, i.e. hypercube vertices which are feasible in (1) and such that all their adjacent hypercube vertices are also feasible in (1) and exterior points, for which there is at least one infeasible adjacent hypercube verte...

In each iteration of the interior point method (IPM) at least one linear system has to be solved. The main computational effort of IPMs consists in the computation of these linear systems. Solving the corresponding linear systems with a direct method becomes very expensive for large scale problems. In this thesis, we have been concerned with using an iterative method for solving the reduced KKT...

In this paper, we present global and local convergence results for an interior-point method for nonlinear programming and analyze the computational performance of its implementation. The algorithm uses an `1 penalty approach to relax all constraints, to provide regularization, and to bound the Lagrange multipliers. The penalty problems are solved using a simplified version of Chen and Goldfarb’...

This work concerns primal-dual interior-point methods for semideenite programming (SDP) that use a search direction originally proposed by Helmberg-Rendl-Vanderbei-Wolkowicz 5] and Kojima-Shindoh-Hara 11], and recently rediscovered by Monteiro 15] in a more explicit form. In analyzing these methods, a number of basic equalities and inequalities were developed in 11] and also in 15] through diie...

DSDP implements the dual-scaling algorithm for semidefinite programming. The source code if this interior-point solver, written entirely in ANSI C, is freely available. The solver can be used as a subroutine library, as a function within the MATLAB environment, or as an executable that reads and writes to files. Initiated in 1997, DSDP has developed into an efficient and robust general purpose ...

The use of computer simulations has revolutionized the way engineers design and improve products and affects all design stages from concept to realization. As a consequence optimization has become an important tool for the engineer to realize better designs without the need of extensive prototype building. One of the algorithms that has shown an important ability to deal with this type of optim...

We study interior operators and interior structures in a fuzzy setting.We investigate systems of “almost open” fuzzy sets and the relationshipsto fuzzy interior operators and fuzzy interior systems.