This article provides a synopsis of the major developments in interior point methods for
mathematical programming in the last thirteen years, and discusses current and future …

This book gathers threads that have evolved across different mathematical disciplines into
seamless narrative. It deals with condition as a main aspect in the understanding of the …

We study the situation in which, having solved a linear program with an interior-point
method, we are presented with a new problem instance whose data is slightly perturbed …

We present an exact rational solver for mixed-integer linear programming that avoids the
numerical inaccuracies inherent in the floating-point computations used by existing software …

A conic linear system is a system of the form¶ P (d): find x that solves b-Ax∈ CY, x∈ CX,¶
where CX and CY are closed convex cones, and the data for the system is d=(A, b). This …

A conic linear system is a system of the form¶¶(FP d) Ax= b¶ x∈ CX,¶¶ where A: X? Y is a
linear operator between n-and m-dimensional linear spaces X and Y, b∈ Y, and CX⊂ X is a …

In this paper we consider the parameter space of all the linear inequality systems, in the n-
dimensional Euclidean space, with a fixed and arbitrary (possibly infinite) index set. This …

Reoptimization techniques for an interior point method applied to solving a sequence of
linear programming problems are discussed. Conditions are given for problem perturbations …

The modern theory of condition measures for convex optimization problems was initially
developed for convex problems in the conic format (CP_d)\qquad\z_*:=\min_x{c^tx|Ax …

In recent years, a body of research into" condition numbers" for convex optimization has
been developed, aimed at capturing the intuitive notion of problem behavior. This research …