Abstract By using a constant step-size, the convergence analysis of the gradient projection method on the sphere is presented for a closed spherically convex set. This algorithm is applied to discuss copositivity of operators with respect to cones. This approach can also be used to analyse solvability of nonlinear cone-complementarity problems. To our best knowledge this is the first numerical method related to the copositivity of operators with respect to the positive semidefinite cone. Numerical results concerning the copositivity of operators are also provided.

Process manufacturing is increasingly being driven by market forces, customer needs, and perceptions, resulting in more and more complex multiproduct manufacturing technologies. The increasing automation and tighter quality constraints related to these processes make the operator's job more and more difficult. This makes decision support systems (DSSs) for the operator more important than ever before. A traditional operator support system (OSS) focuses only on specific tasks that are performed. In the case of complex processes, the design of an integrated information system is extremely important. The proposed data-warehouse-based OSS makes possible linking complex and isolated production units based on the integration of the heterogenous information collected from the production units of a complex production process. The developed OSS is based on a data warehouse designed by following the proposed focus-on-process data-warehouse-design approach, which means stronger focus on the material and information flow through the entire enterprise. The resulting OSS follows the process through the organization instead of focusing separate tasks of the isolated process units. For human-computer interaction, front-end tools have been worked out, where exploratory data analysis and advanced multivariate statistical models are applied to extract the most informative features of the operation of the technology. The concept is illustrated by an industrial case study, where the OSS is designed for the monitoring and control of a high-density polyethylene (HDPE) plant.