In semidefinite programming, one minimizes a linear function subject to the constraint that an affine combination of symmetric matrices is positive semidefinite. Such a constraint is nonlinear andâ€¦ (More)

In a second-Order cone program (SOCP) a linear function is minimized over the intersection of an affine set and the product of second-Order (quadratic) cones. SOCPs are nonlinear convex Problems thatâ€¦ (More)

A geometric program (GP) is a type of mathematical optimization problem characterized by objective and constraint functions that have a special form. Recently developed solution methods can solveâ€¦ (More)

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,â€¦ (More)

Several important problems in control theory can be reformulated as semidefinite programming problems, i.e., minimization of a linear objective subject to Linear Matrix Inequality (LMI) constraints.â€¦ (More)

The nuclear norm (sum of singular values) of a matrix is often used in convex heuristics for rank minimization problems in control, signal processing, and statistics. Such heuristics can be viewed asâ€¦ (More)

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 asâ€¦ (More)

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 asâ€¦ (More)