Railway passenger transportation plays a fundamental role in Europe, particularly in view of the growing number of trains offering valuable services such as high speed travel, high comfort, etc. Hence, it is advantageous to submit seat inventories to a Yield Management system to get the maximum revenue. We consider a deterministic linear programming model and a probabilistic nonlinear programming model for the network problem with non-nested seat allocation. A first comparative analysis of the computational results obtained by the two models, both in terms of the overall expected revenue and in terms of CPU time, is carried out. Furthermore, we describe a new nonlinear algorithm for the solution of the probabilistic nonlinear programming model that exploits the structure of the optimization problem. The numerical results obtained on a set of real data show that, for this class of problems, this algorithm is more efficient than other standard algorithms for nonlinear programming problems.

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In this paper we consider the problem of minimizing a (possibly nonconvex) quadratic function with a quadratic constraint. We point out some new properties of the problem. In particular, in the rst part of the paper, we show that (i) given a KKT point that is not a global minimizer, it is easy to nd a \better" feasible point; (ii) strict complementarity holds at the local-nonglobal minimizer. In the second part, we show that the original constrained problem is equivalent to the unconstrained minimization of a piecewise quartic merit function. Using the unconstrained formulation we give, in the nonconvex case, a new second order necessary condition for global minimizers. In the third part, algorithmic applications of the preceding results are brie y outlined and some preliminary numerical experiments are reported.

Many real applications can be formulated as nonlinear minimization problems with a single linear equality constraint and box constraints. We are interested in solving problems where the number of variables is so huge that basic operations, such as the evaluation of the objective function or the updating of its gradient, are very time consuming. Thus, for the considered class of problems (including dense quadratic programs), traditional optimization methods cannot be applied directly. In this paper, we define a decomposition algorithm model which employs, at each iteration , a descent search direction selected among a suitable set of sparse feasible directions. The algorithm is characterized by an acceptance rule of the updated point which on the one hand permits to choose the variables to be modified with a certain degree of freedom and on the other hand does not require the exact solution of any subproblem. The global convergence of the algorithm model is proved by assuming that the objective function is continuously differentiable and that the points of the level set have at least one component strictly between the lower and upper bounds. Numerical results on large-scale quadratic problems arising in the training of support vector machines show the effectiveness of an implemented decomposition scheme derived from the general algorithm model. Communicated by P. Tseng.

A new method for the solution of minimization problems with simple bounds is presented. Global convergence of a general scheme requiring the approximate solution of a single linear system at each iteration is proved and a superlinear convergence rate is established without requiring the strict complementarity assumption. The algorithm proposed is based on a simple, smooth unconstrained reformulation of the bound constrained problem and may produce a sequence of points that are not feasible. Numerical results are reported.