Abstract. The problem of maximizing the determinant of a matrix subject to linear matrix inequalities arises in many elds, including computational geometry, statistics, system identi cation, experiment design, and information and communication theory. It can also be considered as a generalization of the semide nite programming problem.We give a n o v erview of the applications of the determinant maximization problem, pointing out simple cases where specialized algorithms or analytical solutions are known. We then describe an interior-point method, with a simpli ed analysis of the worst-case complexity and numerical results that indicate that the method is very e cient, both in theory and in practice. Compared to existing specialized algorithms where they are available, the interior-point method will generally be slower; the advantage is that it handles a much wider variety of problems.

We consider the design of nite impulse response FIR lters subject to upper and lower bounds on the frequency response magnitude. The associated optimization problems, with the lter coe cients as the variables and the frequency response bounds as constraints, are in general nonconvex. Using a change of variables and spectral factorization, we can pose such problems as linear or nonlinear convex optimization problems. As a result we can solve them e ciently and globally by recently developed interior-point methods. We describe applications to lter and equalizer design, and the related problem of antenna array w eight design.

No abstract

We present a new semide nite programming approach to FIR lter design with arbitrary upper and lower bounds on the frequency response magnitude. It is shown that the constraints can be expressed as linear matrix inequalities LMIs, and hence they can be easily handled by recent interior-point methods. Using this LMI formulation, we can cast several interesting lter design problems as convex or quasi-convex optimization problems, e.g., minimizing the length of the FIR lter and computing the Chebychev approximation of a desired power spectrum or a desired frequency response magnitude on a logarithmic scale.

No abstract