Abstract In this paper we propose iterative solvers for portfolio optimization in a two dimensional domain. To put the modeled equations into practice we provide Jacobi and Gauss-Seidal algorithms. In order to improve the efficiency of portfolio optimization iterative solvers we study the convergence rate and introduce successive over relaxation scheme to the developed algorithms. Further to overcome the domain bias of this relaxation scheme we propose a symmetric successive relaxation model. This is demonstrated through a Chebyshev acceleration technique. We conclude by stating that iterative solvers are more superior and consistent techniques for portfolio optimization. Keywords: Iterative solvers, portfolio optimization, successive over relaxation, Chebyshev accelaration, Jacobi and Gauss-Seidel algorithms Iterative Solvers for Portfolio Optimization Anandadeep Mandal 1. Introducion Markowitz pioneered portfolio optimization in his seminal paper in 1952. Since then there has been lot of research in his ield related to the development of portfolio optimization models. The basic fundamentals of portfolio optimization are: a) modeling of risk and utility constraints and b) addressing eficiency parameter of the model as the portfolio is subjected to wide variety of instrument and scenario. Authors developed several models for addressing and modeling the above issues related to portfolio optimization. Konno and Wijayanayake (1999) developed the mean absolute deviation approach, Dembo and Rosen (1999) formulated the regret optimization approach and Young (1998) devised the minimax technique. The eficiency of the models using linear programming techniques showed better performance than the quadratic programming approach proposed by Markowitz. Rockafellar and Uryasev (2000) stated that the linear programming methodology can be used for Tail Value- at-Risk or termed as Conditional Value-at-Risk (CVaR). Uryasev (2000) highlighted in his paper the need to generate equation of constraints for optimization of problems using CVaR. Various authors including Dufie and Pan (1997), Pritsker (1997), Simons (1996) and Stambaugh (1996) have evaluated VaR through linear estimation of portfolio risk under log-normal distribution of underlying constraints. In case of portfolios with optians, other techniques involving Monte Carlo simulations can be effectively used. Bucay and Rosen (1999), Mausser and Rosen (1991) and Stublo Beder (1995) have highlighted the use of simulation in portfolio optimization. * Anandadeep Mandal, Doctoral Scholar, Cranield School of Management, Cranield University, England, United Kingdom