Displaying similar documents to “A new barrier for a class of semidefinite problems”

On the central paths and Cauchy trajectories in semidefinite programming

Julio López, Héctor Ramírez C. (2010)

Kybernetika

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In this work, we study the properties of central paths, defined with respect to a large class of penalty and barrier functions, for convex semidefinite programs. The type of programs studied here is characterized by the minimization of a smooth and convex objective function subject to a linear matrix inequality constraint. So, it is a particular case of convex programming with conic constraints. The studied class of functions consists of spectrally defined functions induced by penalty...

A numerical feasible interior point method for linear semidefinite programs

Djamel Benterki, Jean-Pierre Crouzeix, Bachir Merikhi (2007)

RAIRO - Operations Research

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This paper presents a feasible primal algorithm for linear semidefinite programming. The algorithm starts with a strictly feasible solution, but in case where no such a solution is known, an application of the algorithm to an associate problem allows to obtain one. Finally, we present some numerical experiments which show that the algorithm works properly.

A logarithm barrier method for semi-definite programming

Jean-Pierre Crouzeix, Bachir Merikhi (2008)

RAIRO - Operations Research

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This paper presents a logarithmic barrier method for solving a semi-definite linear program. The descent direction is the classical Newton direction. We propose alternative ways to determine the step-size along the direction which are more efficient than classical line-searches.

An analytic center cutting plane algorithm for finding equilibrium points

Fernanda M.P. Raupp, Wilfredo Sosa (2006)

RAIRO - Operations Research

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We present a variant of the analytic center cutting plane algorithm proposed by Goffin  (1996) to approximately solve equilibrium problems as proposed by Blum and Oettli (1994), which include as particular problems the variational inequalities problem, the Nash equilibria problem in non-cooperative games, the convex minimization problem, and the fixed point problem. Furthermore, we analyze the convergence and complexity of the modified algorithm.