The problem of maximizing the determinant of a matrix subject to linear matrix inequalities
(LMIs) arises in many fields, including computational geometry, statistics, system …

Semidefinite programming has been described as linear programming for the year 2000. It is
an exciting new branch of mathematical programming, due to important applications in …

We present a dual-scaling interior-point algorithm and show how it exploits the structure and
sparsity of some large-scale problems. We solve the positive semidefinite relaxation of …

A number of important problems from system and control theory can be numerically solved
by reformulating them as convex optimization problems with linear matrix inequality (LMI) …

We consider a new nonlinear relaxation for the Constrained Maximum-Entropy Sampling
Problem {the problem of choosing the ss principal submatrix with maximal determinant from …

This thesis deals with algorithms for a subclass of nonlinear, convex optimization problems,
namely semidefinite programs. In order place the topics which are dealt with in perspective …

We consider a new nonlinear relaxation for the Constrained Maximum Entropy Sampling
Problem—the problem of choosing the s× s principal submatrix with maximal determinant …

We build upon the work of Fukuda et al. SIAM J. Optim., 11 (2001), pp. 647--674 and Nakata
et al. Math. Program., 95 (2003), pp. 303--327, in which the theory of partial positive …

Let Sn be the space of nxn real symmetric matrices, and for A, BE Sn, A• B denotes the inner
product Li, j Aij Bij, and we write A~ B if AB is positive semidefinite. Suppose that Qo,..., Qm E …

We use the semidefinite relaxation to approximate combinatorial and quadratic optimization
problems subject to linear, quadratic, as well as boolean constraints. We present a dual …