The extended Ritz method for functional optimization: overview and applications to single-person and team optimal decision problems

Abstract

To cite this Article Baglietto, M., Sanguineti, M. and Zoppoli, R.( 2009)'The extended Ritz method for functional optimization: overview and applications to single-person and team optimal decision problems',Optimization Methods and Software,24:1,15 -43

Optimization based on quasi-Monte Carlo sampling to design state estimators for non-linear systems

“…Such sequences generate sampling grids in the spaces of the system state and error estimate, which optimize 'how uniformly' the points are spread. These sequences were successfully used in complex optimization tasks [4,[7][8][9].…”

Smooth Optimal Decision Strategies for Static Team Optimization Problems and Their Approximations

“…We are currently investigating the extension of such results to other nonlinear approximation schemes with sigmoidal and spline computational units. The numerical results in [2][3][4] show that often these approximation schemes (which belong to the wider family of variable-basis approximation schemes [15,16]) are able to find accurate suboptimal solutions to team optimization problems with high-dimensional states, using a small number of parameters to be optimized. Variable-basis approximation schemes have been successfully exploited also in other optimization tasks (see the references in [30,31]).…”

“…Figure 1 gives an idea of a network team optimization problem modeling a store-and-forward packet-switching telecommunication network (see [2,4]). Suppose that the DMs are n routers acting as members of a same team (i.e., they aim to maximize a common objective, decomposable into the sum of several individual objectives related, e.g., to the congestion of the links).…”