Abstract We consider primal-dual pairs of semidefinite programs and assume that they are singular, i.e., both primal dual either weakly feasible or infeasible. Under such circumstances, strong duality may break down the might have a nonzero gap. Nevertheless, there arbitrary small perturbations to problem data which would make them strongly thus zeroing In this paper, we conduct an asymptotic a...

Standard interior-point algorithms usually show a poor performance when applied to multicommodity network flows problems. A recent specialized interior-point algorithm for linear multicommodity network flows overcame this drawback, and was able to efficiently solve large and difficult instances. In this work we perform a computational evaluation of an extension of that specialized algorithm for...

Interior point methods and random walk approaches have been long considered disparate approaches for convex optimization. We show how simulated annealing, one of the most common random walk algorithms, is equivalent, in a certain sense, to the central path interior point algorithm applied to the entropic universal barrier function. Using this observation we improve the state of the art in polyn...

This paper describes a novel approach to recovering a parametric deformation that optimally registers one image to another. The method proceeds by constructing a global convex approximation to the match function which can be optimized using interior point methods. The paper also describes how one can exploit the structure of the resulting optimization problem to develop efficient and effective ...

In this paper, we describe our implementation of a primal-dual infeasible-interior-point algorithm for large-scale linear programming under the MATLAB 1 environment. The resulting software is called LIPSOL { Linear-programming Interior-Point SOLvers. LIPSOL is designed to take the advantages of MATLAB's sparse-matrix functions and external interface facilities, and of existing Fortran sparse Ch...

It is well known that convex SQP subproblems with a Euclidean norm trust region constraint can be reduced to second order cone programs for which the theory of Euclidean Jordan-algebras leads to efficient interior-point algorithms. Here, a brief and self-contained outline of the principles of such an implementation is given. All identities relevant for the implementation are derived from scratc...

Constraint-reduction schemes have been proposed for the solution by interior-point methods of linear programs with many more inequality constraints than variables in standard dual form. Such schemes have been shown to be provably convergent and highly efficient in practice. A critical requirement of these schemes is the availability of an initial dual-feasible point. In this paper, building on ...

This paper demonstrates how interior-point methods can use multiple processors efficiently to solve large semidefinite programs that arise in VLSI design, control theory, and graph coloring. Previous implementations of these methods have been restricted to a single processor. By computing and solving the Schur complement matrix in parallel, multiple processors enable the faster solution of medi...