Stat Optim Inf Comput

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 |-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.CC999999/ImCDC/Intramural CDC HHSUnited States/2022-01-01T00:00:00Z34141814PMC820532010747vault:3716

Multicast Multigroup Beamforming under Per-antenna Power Constraints

Linear precoding exploits the spatial degrees of freedom offered by multi-antenna transmitters to serve multiple users over the same frequency resources. The present work focuses on simultaneously serving multiple groups of users, each with its own channel, by transmitting a stream of common symbols to each group. This scenario is known as physical layer multicasting to multiple co-channel groups. Extending the current state of the art in multigroup multicasting, the practical constraint of a maximum permitted power level radiated by each antenna is tackled herein. The considered per antenna power constrained system is optimized in a maximum fairness sense. In other words, the optimization aims at favoring the worst user by maximizing the minimum rate. This Max-Min Fair criterion is imperative in multicast systems, where the performance of all the receivers listening to the same multicast is dictated by the worst rate in the group. An analytic framework to tackle the Max-Min Fair multigroup multicasting scenario under per antenna power constraints is therefore derived. Numerical results display the accuracy of the proposed solution and provide insights to the performance of a per antenna power constrained system.Comment: Presented in IEEE ICC 2014, Sydney, AUS. arXiv admin note: substantial text overlap with arXiv:1406.755

COSMO: A conic operator splitting method for convex conic problems

This paper describes the Conic Operator Splitting Method (COSMO) solver, an operator splitting algorithm for convex optimisation problems with quadratic objective function and conic constraints. At each step the algorithm alternates between solving a quasi-definite linear system with a constant coefficient matrix and a projection onto convex sets. The low per-iteration computational cost makes the method particularly efficient for large problems, e.g. semidefinite programs that arise in portfolio optimisation, graph theory, and robust control. Moreover, the solver uses chordal decomposition techniques and a new clique merging algorithm to effectively exploit sparsity in large, structured semidefinite programs. A number of benchmarks against other state-of-the-art solvers for a variety of problems show the effectiveness of our approach. Our Julia implementation is open-source, designed to be extended and customised by the user, and is integrated into the Julia optimisation ecosystem.Comment: 45 pages, 11 figure

A Full-NT Step Infeasible Interior-Point Algorithm for Mixed Symmetric Cone LCPs

An infeasible interior-point algorithm for mixed symmetric cone linear complementarity problems is proposed. Using the machinery of Euclidean Jordan algebras and Nesterov-Todd search direction, the convergence analysis of the algorithm is shown and proved. Moreover, we obtain a polynomial time complexity bound which matches the currently best known iteration bound for infeasible interior-point methods