485 research outputs found
Convergence analysis of an Inexact Infeasible Interior Point method for Semidefinite Programming
In this paper we present an extension to SDP of the well known infeasible Interior Point method for linear programming of Kojima,Megiddo and Mizuno (A primal-dual infeasible-interior-point algorithm for Linear Programming, Math. Progr., 1993). The extension developed here allows the use of inexact search directions; i.e., the linear systems defining the search directions can be solved with an accuracy that increases as the solution is approached. A convergence analysis is carried out and the global convergence of the method is prove
Interior point methods : current status and future directions
Cover title.Includes bibliographical references (leaves 23-24).Robert Freund and Shinji Mizuno
Interior point methods : current status and future directions
Cover title.Includes bibliographical references (leaves 23-24).Robert Freund and Shinji Mizuno
Real and Complex Monotone Communication Games
Noncooperative game-theoretic tools have been increasingly used to study many
important resource allocation problems in communications, networking, smart
grids, and portfolio optimization. In this paper, we consider a general class
of convex Nash Equilibrium Problems (NEPs), where each player aims to solve an
arbitrary smooth convex optimization problem. Differently from most of current
works, we do not assume any specific structure for the players' problems, and
we allow the optimization variables of the players to be matrices in the
complex domain. Our main contribution is the design of a novel class of
distributed (asynchronous) best-response- algorithms suitable for solving the
proposed NEPs, even in the presence of multiple solutions. The new methods,
whose convergence analysis is based on Variational Inequality (VI) techniques,
can select, among all the equilibria of a game, those that optimize a given
performance criterion, at the cost of limited signaling among the players. This
is a major departure from existing best-response algorithms, whose convergence
conditions imply the uniqueness of the NE. Some of our results hinge on the use
of VI problems directly in the complex domain; the study of these new kind of
VIs also represents a noteworthy innovative contribution. We then apply the
developed methods to solve some new generalizations of SISO and MIMO games in
cognitive radios and femtocell systems, showing a considerable performance
improvement over classical pure noncooperative schemes.Comment: to appear on IEEE Transactions in Information Theor
A semidefinite programming approach for the projection onto the cone of negative semidefinite symmetric tensors with applications to solid mechanics
We propose an algorithm for computing the projection of a symmetric
second-order tensor onto the cone of negative semidefinite symmetric tensors
with respect to the inner product defined by an assigned positive definite
symmetric fourth-order tensor C. The projection problem is written as a
semidefinite programming problem and an algorithm based on a primal-dual
path-following interior point method coupled with a Mehrotra's
predictor-corrector approach is proposed. Implementations based on direct
methods are theoretically and numerically investigated taking into account
tensors C arising in the modelling of masonry-like materials
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