A user-friendly free Matlab package for defining Linear Matrix Inequality (LMI) problems. 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: (1) Declare an LMI problem. Five Matlab functions allow to define completely an LMI problem which can be characterised by variables, inequality constraints and a linear objective: * Initialise the LMI problem: sdmpb. * Declare the matrix variables: sdmvar. * Declare the inequality constraints: sdmlmi and sdminequ. * Declare the linear objective: sdmobj. (2) Solve an LMI problem. A unique function, sdmsol, calls the SeDuMi solver. Options allow to tune the solver parameters. (3) Modify an LMI problem. At any moment it is possible to append an LMI problem by adding variables, inequalities or linear terms to the objective. Moreover, the sdmset function allows to freeze matrix variables to specified values. (4) 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 inequality constraints are satisfied.
Technical report number 01445 LAAS-CNRS : 7 av. du Colonel Roche, 31077 Toulouse Cedex 4, FRANCE November 2001