(27a) Global Optimization Based on Modified Generalized Reduced Gradiant and Its Application on Interval Analysis

Authors: 
Xu, G., Invensys/SimSci-Esscor
Stadtherr, M. A., University of Notre Dame


Reliable solution algorithms for global optimization, such as Interval Analysis, had been introduced to find all the stationary points (solutions) within given domain. However, performance remains as a challenging problem. This presentation introduces a new solving strategy by connecting Generalized-Reduced-Gradient algorithm and Interval Analysis. The new method, which is based on bi-level iterative scheme, has the potential to reduce the number of variables as well as simplify the problem specifications without losing the promise of finding all the solutions within given domain.

The problem for bi-level iteration is that it is known for its jacobian complexity as well as restrained solution path. Thus, one may select single-level iteration depending on the problem specifications. It has been found, however, that the performance for global solution method depends as much as (or even more) on the problem dimensionality than on the problem complexity. Meanwhile, simple or even linear constraints exist for majority optimization problems. Thus, if inner-level scheme can be defined not only simple but also reducing the problem dimension, then applying global optimization for certain bi-level iteration problems can provide both reliability and efficency.

The way to modify interval analysis on bi-level iteration is discussed and preliminary tests is done by this presentation. This is also the first time a rigorous bi-level iterative modification on interval analysis is addressed.