A Study on 1-D Simplex Search Algorithm with its Numerical Experiments Through Computer Algebra

Abstract

Computer techniques have been developed to solve 1-D NLP problems. The 1-D simplex search algorithm was studied and a code corresponding to the modified phase-0 has been developed. The 1-D two phase methods and modified Phase-0 method have been compared with those reported by others. The efficiency of computer techniques and algorithms have been demonstrated with a number of numerical examples.

An Algorithmic Technique for Solving Non-Linear Programming and Quadratic Programming Problems

“…We also briefly discuss the formulation of QP and NLP problems which has shown the necessity for developing a uniform technique. Das 4,5] In this section, we discuss the 1-D simplex search methods for finding the optimum solutions and also present two flowcharts of Choo & Kim two phase method in H. K. Das & Hasan [4].…”

“…It is extremely difficult to state that one method is definitely superior to another method without analytical or numerical experimental investigation. On the other hand, in this research, we find the prescribed paper [4,5,6,7] which is successful in particular type of NLP problems and so we have modified this algorithm into a single framework successfully by developing a new computer technique. Finally, we develop a computer technique for those types of NLP problems.…”

“…Later, in 2013, Das and Hasan [4] developed a generalized computer technique for solving unconstrained NLP problems. Recently, in 2014, Das, Saha & Hasan [5] have studied on the 1-D Simplex Search and showed some merits and demerits in 1-D methods through numerical experiments. But all of them are silent about QP problems and the uniform computer technique.…”