A Generalized Computer Technique for Solving Unconstrained Non-Linear Programming Problems

Abstract

An unconstrained problem with nonlinear objective function has many applications. This is often viewed as a discipline in and of itself. In this paper, we develop a computer technique for solving nonlinear unconstrained problems in a single framework incorporating with Golden section, Gradient Search method. For this, we first combine this algorithm and then develop a generalized computer technique using the programming language MATHEMATICA. We demonstrate our computer technique 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].…”

“…In 1987 this method was proposed by Choo and Kim which is one of the most robust and efficient 1-D direct search methods which had been analyzed in H. K. Das and Hasan [3,4].…”

“…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.…”

“…In 2012, Datta & Hasan [6,7] developed computer technique for the Lagrange method and Karush-Kuhn-Tucker Method. 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.…”

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

“…Das et al 5 developed a computer technique incorporated with Golden section and Gradient search methods which is very powerful for the given optimal interval but if a proper optimal interval is not chosen it should face a complexity to find the optimal solution like Choo et al 3 . In the current research, the complexity of the Choo et al 3 and Das et al 5 has been removed by an uniform algorithm of the Choo et al 3 and as proposed by Ayode 6 modified phase-0.…”