Because of their versatility and robustness, numerical continuation or path following
methods have been finding ever wider use in scientific applications. Our aim here is to give …

A new methodology for constructing convex optimization models called disciplined convex
programming is introduced. The methodology enforces a set of conventions upon the …

In semidefinite programming, one minimizes a linear function subject to the constraint that
an affine combination of symmetric matrices is positive semidefinite. Such a constraint is …

This paper gives an approach to implementing a second-order primal-dual interior point
method. It uses a Taylor polynomial of second order to approximate a primal-dual trajectory …

This book was intended as an introduction to the topic of numerical continuation which
would be accessible to a readership of widely varying mathematical backgrounds. Realizing …

The first comprehensive review of the theory and practice of one oftoday's most powerful
optimization techniques. The explosive growth of research into and development of …

This paper provides a theoretical foundation for efficient interior-point algorithms for convex
programming problems expressed in conic form, when the cone and its associated barrier …

This book aims at developing a thorough understanding of the most general theory for
interior-point methods, a class of algorithms for convex optimization problems. The study of …

This note summarizes a report with the same title, where a study was carried out regarding a
unified approach, proposed by Kojima, Mizuno and Yoshise, for interior point algorithms for …

We present an O (√ nL)-iteration homogeneous and self-dual linear programming (LP)
algorithm. The algorithm possesses the following features:• It solves the linear programming …