Second-order cone programming (SOCP) problems are convex optimization problems in
which a linear function is minimized over the intersection of an affine linear manifold with the …

The modern era of interior-point methods dates to 1984, when Karmarkar proposed his
algorithm for linear programming. In the years since then, algorithms and software for linear …

The Handbook of Linear Algebra provides comprehensive coverage of linear algebra
concepts, applications, and computational software packages in an easy-to-use handbook …

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 …

The low-rank semidefinite programming problem LRSDP r is a restriction of the semidefinite
programming problem SDP in which a bound r is imposed on the rank of X, and it is well …

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 …

A critical disadvantage of primal-dual interior-point methods compared to dual interior-point
methods for large scale semidefinite programs (SDPs) has been that the primal positive …

In this paper we show that the so-called commutative class of primal-dual interior point
algorithms which were designed by Monteiro and Zhang for semidefinite programming …

We present a dual-scaling interior-point algorithm and show how it exploits the structure and
sparsity of some large-scale problems. We solve the positive semidefinite relaxation of …

Die hier angesprochene Unterscheidung zwischen stetigen und diskreten Problemen ergibt
sich aus den sehr unterschiedlichen Lösungsansätzen. Grob gesprochen kann man bei …