A Globally Convergent Infeasible Interior Point Method for Linear Constrained Convex Programming

R.Q. do Nascimento and P. R. Oliveira

We present an infeasible interior point method for linear constrained convex programming, which has finite convergence for an epsilon-solution. The method is a variant of the infeasible interior point method developed for linear programming. An interesting fact is that when the primal problem is consistent, its dual is asymptotically consistently feasible and, if the matrix A has full rank, the sequence generated by the algorithm is bounded. The results obtained on the boundedness were based on the theory developed for monotone operators and complementarity problems, besides some hypothesis on asymptotic consistency sequences and boundedly asymptotically solvable problems. This method was very efficient when solving problems of geometric programming in literature.

R.T. PESC/COPPE-Federal University of Rio de Janeiro C.P. 68511, 20771-421, Rio de Janeiro, Brazil, 04/2000

Contact: poliveir@cos.ufrj.br