Adaptive projection methods for linear fractional programming

In this paper, we are interested in solving a linear fractional program by two different approaches. The first one is based on interior point methods which makes it possible to solve an equivalent linear program to the linear fractional program. The second one allows us to solve a variational inequalities problem equivalent to the linear fractional program by an efficient projection method. The numerical tests show clearly that interior point methods are more efficient than of projection one.

Global Minimization for Generalized Polynomial Fractional Program

This paper is concerned with an efficient global optimization algorithm for solving a kind of fractional program problem(P), whose objective and constraints functions are all defined as the sum of ratios generalized polynomial functions. The proposed algorithm is a combination of the branch-and-bound search and two reduction operations, based on an equivalent monotonic optimization problem of(P). The proposed reduction operations specially offer a possibility to cut away a large part of the currently investigated region in which the global optimal solution of(P)does not exist, which can be seen as an accelerating device for the solution algorithm of(P). Furthermore, numerical results show that the computational efficiency is improved by using these operations in the number of iterations and the overall execution time of the algorithm, compared with other methods. Additionally, the convergence of the algorithm is presented, and the computational issues that arise in implementing the algorithm are discussed. Preliminary indications are that the algorithm can be expected to provide a practical approach for solving problem(P)provided that the number of variables is not too large.

Two types of duality in multiobjective fractional programming

In this paper, we tire concerned with duality of a multiobjective fractional program. Two different dual problems are introduced with respect to the primal multiobjective fractional program. Under a mild assumption, we prove a weak duality theorem and a strong duality theorem for each type of duality. Finally, we explore some relations between these two types of duality.