Monotonicity Analysis and the Reduced Gradient Method in Constrained Optimization

Abstract

The concept of monotonicity analysis is combined with the reduced gradient technique for design optimization. The combination is based on a strategy for applying monotonicity analysis in specified search directions and incorporates this strategy into an iterative procedure for identifying the active inequality constraints in an optimization problem. As the active constraints are identified, the reduced gradient information based on these constraints forms the basis for a variable metric search leading to the constrained optimum. Test results are presented which indicate the performance of two different algorithms using this approach.