User ’ s Guide for SEDUMI INTERFACE 1 . 04

This report describes a user-friendly MATLAB package for defining Linear Matrix Constraints (LMCs). It acts as an interface for the Self-Dual-Minimisation package (SEDUMI) developed by Jos F. Sturm. The functionalities of SEDUMI INTERFACE are the following: Declare an LMC problem. Five MATLAB functions allow to define completely an LMC problem which can be characterised by scalar and matrix variables, linear matrix equality (LME) constraints, linear matrix inequality (LMI) constraints and a linear objective: – Initialise the LMC problem: sdmpb. – Declare the matrix variables: sdmvar. – Declare the block partitioned equality constraints: sdmlme and sdmequ. – Declare the block partitioned inequality constraints: sdmlmi and sdminequ. – Declare the linear objective: sdmobj. Solve an LMC problem. A unique function, sdmsol, calls the SEDUMI solver. Options allow to tune the solver parameters. Modify an LMC problem. At any moment it is possible to append an LMC problem by adding variables, inequalities or linear terms to the objective. Moreover, the sdmset function allows to freeze matrix variables to specified values. Analyse the solution issued from the solver. For all (feasible or not) problems, the solver outputs the last computed iterate (sdmget). SEDUMI INTERFACE allows to analyse this result in a convivial display. The solution is displayed directly in matrix format and indicators show which constraints are satisfied. This document is an update with respect to SEDUMI INTERFACE 1.01 [23], [22], SEDUMI INTERFACE 1.02 [17] and SEDUMI INTERFACE 1.03 . The last major modifications concern the blocks partitioning of LMCs, the maximisation of Trace BX where B is a data matrix and the increase of LMC problem construction speed. SEDUMI INTERFACE 1.04: Copyright c 2002 Dimitri Peaucelle & Krysten Taitz. This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

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