Abstract A global optimization approach for solving non-monotone equilibrium problems (EPs) is proposed. The class of (regularized) gap functions is used to reformulate any EP as a constrained global optimization program and some bounds on the Lipschitz constant of such functions are provided. The proposed global optimization approach is a combination of an improved version of the algorithm, which exploits local bounds of the Lipschitz constant of the objective function, with local minimizations. Unlike most existing solution methods for EPs, no monotonicity-type condition is assumed in this paper. Preliminary numerical results on several classes of EPs show the effectiveness of the approach.

Hospitals are huge and complex systems. However, for many years, the management was commonly focused on improving the quality of the medical care, while less attention was usually devoted to operation management. In recent years, the need of containing the costs while increasing the competitiveness along with the new policies of National Health Service hospital financing forced hospitals to necessarily improve their operational efficiency. In this paper, we focus on a management problem usually arising in health care. In particular, we deal with optimal resource allocation of a ward of a big hospital. To this aim, we propose a simulation-based optimization approach that makes use of a discrete-event simulation model, reproducing the hospital services and combined with a derivative-free multiobjective optimization method. The results obtained on the obstetrics ward of an Italian hospital are reported, showing the effectiveness of the new approach proposed.

MOTIVATION: The identification of cell cycle-regulated genes through the cyclicity of messenger RNAs in genome-wide studies is a difficult task due to the presence of internal and external noise in microarray data. Moreover, the analysis is also complicated by the loss of synchrony occurring in cell cycle experiments, which often results in additional background noise. RESULTS: To overcome these problems, here we propose the LEON (LEarning and OptimizatioN) algorithm, able to characterize the 'cyclicity degree' of a gene expression time profile using a two-step cascade procedure. The first step identifies a potentially cyclic behavior by means of a Support Vector Machine trained with a reliable set of positive and negative examples. The second step selects those genes having peak timing consistency along two cell cycles by means of a non-linear optimization technique using radial basis functions. To prove the effectiveness of our combined approach, we use recently published human fibroblasts cell cycle data and, performing in vivo experiments, we demonstrate that our computational strategy is able not only to confirm well-known cell cycle-regulated genes, but also to predict not yet identified ones. AVAILABILITY AND IMPLEMENTATION: All scripts for implementation can be obtained on request.

Training of support vector machines (SVMs) requires to solve a linearly constrained convex quadratic problem. In real applications, the number of training data may be very huge and the Hessian matrix cannot be stored. In order to take into account this issue, a common strategy consists in using decomposition algorithms which at each iteration operate only on a small subset of variables, usually referred to as the working set. Training time can be significantly reduced by using a caching technique that allocates some memory space to store the columns of the Hessian matrix corresponding to the variables recently updated. The convergence properties of a decomposition method can be guaranteed by means of a suitable selection of the working set and this can limit the possibility of exploiting the information stored in the cache. We propose a general hybrid algorithm model which combines the capability of producing a globally convergent sequence of points with a flexible use of the information in the cache. As an example of a specific realization of the general hybrid model, we describe an algorithm based on a particular strategy for exploiting the information deriving from a caching technique. We report the results of computational experiments performed by simple implementations of this algorithm. The numerical results point out the potentiality of the approach.