On Handling Free Variables in Interior-Point Methods for Conic Linear Optimization

On Handling Free Variables in Interior-Point Methods for Conic Linear Optimization

We revisit a regularization technique of Mészáros for handling free variables within interiorpoint methods for conic linear optimization. We propose a simple computational strategy, supported by a global convergence analysis, for handling the regularization. Using test problems from benchmark suites and recent applications, we demonstrate that the modern code SDPT3 modified to incorporate the p...

Interior Point Methods for Linear Optimization: Exercises

Interior-Point Methods for Linear Optimization

Interior-point methods for optimization

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.

Infeasible constraint-reduced interior-point methods for linear optimization

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 ...