Fast local optimization in decision analytic software

Abstract: In decision analysis, significant recognition has been given to the fact that requiring numerically precise information seems unrealistic for real-life decision situations, Despite the emergence of many modern apporaches, which attempt to handle imprecise estimates, concentration has focused more on representation and less on evaluation. Methods such as the DELTA method  challenged this issue by its evaluation framework that can accommodate both precision an imprecision, and thus pushes forward the disign of advanced dicision analysis systems. However, computationally, DELTA may incur time-consuming calculations due to the introduction of imprecise information into the probability space as well as the value space. Although two fast linear programming based bilinear optimazation algorithms were suggested, which were supporsed to satisfy certain presumed conditions, they are found to be too restrictive.This thesis presents a fast potimization approach that can be viewed as a generalized version of the two fast algorithms. The motivation stems from the attempts to discard those presumed conditions. This approach combines ideas from both matrix computations and linear programming, and is, in fact, an iterative method. Since the DELTA method inteds to compute the difference of two expected utilities, this bilinear optimization issue is non-convex, and thus will certainly touch upon the global optimization area. As previously suggested, actually all methods for global optimization consist of two phases: a global phose to thoroughly explore subsets of the feasible region where it is known the blobal optimum will be found, an a local phase to improve the approximation to some local optima, Basically, this fast algorithm is devoted to the local optimization phase.