Abstract
In this paper, an improved Interior-Point Method (IPM) for solving symmetric optimization problems is presented. Symmetric optimization (SO) problems are linear optimization problems over symmetric cones. In particular, the method can be efficiently applied to an important instance of SO, a Controlled Tabular Adjustment (CTA) problem which is a method used for Statistical Disclosure Limitation (SDL) of tabular data. The presented method is a full Nesterov-Todd step infeasible IPM for SO. The algorithm converges to ε-approximate solution from any starting point whether feasible or infeasible. Each iteration consists of the feasibility step and several centering steps, however, the iterates are obtained in the wider neighborhood of the central path in comparison to the similar algorithms of this type which is the main improvement of the method. However, the currently best known iteration bound known for infeasible short-step methods is still achieved.
Highlights
Interior-Point Methods (IPMs) are theoretically powerful and numerically efficient iterative methods that are based on Newton’s method
The obtained iteration bound coincides with the one derived for linear optimization (LO), where n is replaced by r, the rank of Euclidean Jordan Algebras (EJAs), and matches currently best-known iteration bounds for infeasible IPMs for Symmetric optimization (SO)
We present an infeasible full NT-step IPM for SO that is a generalization of the feasible IPM discussed in [25]
Summary
Interior-Point Methods (IPMs) are theoretically powerful and numerically efficient iterative methods that are based on Newton’s method. The development of IPM presented in this paper was motivated by the desire to provide a theoretical foundation for the efficient solution of the conic formulation of the Controlled Tabular Adjustment (CTA) problem [13]. Our motivation was to design an IPM to solve conic l1-CTA that has good theoretical convergence properties and it is practical to implement which includes the fact that the method can start with any starting point, feasible or infeasible. The general formulations of CTA and conic reformulation will be listed as examples of problems to which the proposed method can be applied. These problems are called symmetric optimization (SO) problems. For an overview of the relevant results, we refer a reader to the monograph on this subject [1] and the references therein
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