By Ugbe, Thomas A.
The exploration of the Response Surface and investigation into the number of Segments, S, for which Optimal Solutions can be obtained, through Super Convergent Line Series (SCLS), of Constrained Programming (Linear, Quadratic and Cubic) Problems, has been done in this work. The Response Surface was explored and partitioned into Segments (Non-overlapping and Overlapping) and Constrained Programming Problems were solved via the Super Convergent Line Series. It was established numerically and analytically that the best number of Segments was 2 (S=2) for Linear Programming Problems, 4 (S=4) for Quadratic Programming Problems and 8 (S=8) for Cubic Programming Problems for the Non-overlapping Segmentation of the Response Surface (all in one iteration). By solving numerically, the best number of Segments was 3 (S=3) for Linear Programming Problems, 5 (S=5) for Quadratic Programming Problems and 2 (S=2) for Cubic Programming Problems for the Overlapping Segmentation of the Response Surface. The designs generated from Non-overlapping Partitions of the Response Surface was D-and G-optimal for the first-order and second-order models, respectively. It was also verified numerically that the best number of Segments was 2 (S=2) for the three-dimensional Linear Programming Problems using Non-overlapping Segmentation of the Response Surface. Real-life Problems were solved to demonstrate the applicability of the method. A JAVA Program was developed for solving the above problems. Furthermore, Segmentation of the Response Surface helps in locating the Optimum direction and the Optimizer in one iteration in contrast with the usual method which solves the same problem in one or more iteration, as the case may be.