Semide nite programming (or SDP) has been one of the most exciting and active research areas in optimization during the 1990s. It has attracted researchers with very diverse backgrounds, includingâ€¦ (More)

The well-known positive real lemma characterizes positive realness of transfer functions of timeinvariant linear systems via the solvability of certain linear matrix inequalities. In this paper, weâ€¦ (More)

We consider the problem of minimizing the sum of a convex function and of p > 1 fractions subject to convex constraints. The numerators of the fractions are positive convex functions, and theâ€¦ (More)

In this paper, we propose an infeasible-interior-point algorithm for solving a primal-dual linear programming problem. The algorithm uses inexact computations for solving a linear system of equationsâ€¦ (More)

We consider the solution of nonlinear programs with nonline ar semidefiniteness constraints. The need for an efficient exploitati n of the cone of positive semidefinite matrices makes the solution ofâ€¦ (More)

We study the sensitivity of solutions of linear semide#nite programs under small arbitrary perturbations of the data. We present an elementary and self-contained proof of the di/erentiability of theâ€¦ (More)

In this article a primal-dual interior-point method for solving linear programs is proposed. A new approach for generating higher-order search directions, and a new method for an eecient higher-orderâ€¦ (More)