This paper discusses computational experiments with linear optimization problems involving semidefinite, quadratic, and linear cone constraints (SQLPs). Many test problems of this type are solved using a new release of SDPT3, a Matlab implementation of infeasible primal-dual path-following algorithms. The software developed by the authors uses Mehrotra-type… (More)
This document describes a new release, version 3.0, of the software SDPT3. This code is designed to solve conic programming problems whose constraint cone is a product of semidefinite cones, second-order cones, and/or nonnegative orthants. It employs a predictor-corrector primal-dual path-following method, with either the HKM or the NT search direction. The… (More)
In this paper we continue the development of a theoretical foundation for efficient primal-dual interior-point algorithms for convex programming problems expressed in conic form, when the cone and its associated barrier are self-scaled (see [NT97]). The class of problems under consideration includes linear programming, semidefinite programming and convex… (More)
This software package is a Matlab implementation of infeasible path-following algorithms for solving standard semideenite programs (SDP). Mehrotra-type predictor-corrector variants are included. Analogous algorithms for the homogeneous formulation of the standard SDP are also implemented. Four types of search directions are available, namely, the AHO, HKM,… (More)
We study different choices of search direction for primal-dual interior-point methods for semidefinite programming problems. One particular choice we consider comes from a specialization of a class of algorithms developed by Nesterov and Todd for certain convex programming problems. We discuss how the search directions for the Nesterov-Todd (NT) method can… (More)
Optimization problems in which the variable is not a vector but a symmetric matrix which is required to be positive semidefinite have been intensely studied in the last ten years. Part of the reason for the interest stems from the applicability of such problems to such diverse areas as designing the strongest column, checking the stability of a differential… (More)
High Dimension Low Sample Size statistical analysis is becoming increasingly important in a wide range of applied contexts. In such situations, it is seen that the popular Support Vector Machine suffers from " data piling " at the margin, which can diminish generalizability. This leads naturally to the development of Distance Weighted Discrimination, which… (More)
This article describes the current state of the art of interior-point methods (IPMs) for convex, conic, and general nonlinear optimization. We discuss the theory, outline the algorithms, and comment on the applicability of this class of methods, which have revolutionized the field over the last twenty years.