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.
In this paper, a new method is proposed for solving the problem in which the objective function is a linear fractional Bounded Variable (LFBV) function, where the constraints functions are in the form of linear inequalities and the variables are bounded. The proposed method mainly based upon the primal dual simplex algorithm. The Linear Programming Bounded Variables (LPBV) algorithm is extended to solve Linear Fractional Bounded Variables (LFBV).The advantages of LFBV algorithm are simplicity of implementation and less computational effort. We also compare our result with programming language MATHEMATICA.DOI: http://dx.doi.org/10.3329/dujs.v60i2.11522 Dhaka Univ. J. Sci. 60(2): 223-230, 2012 (July)
In this paper, we study the methodology of primal dual solutions in Linear Programming (LP) & Linear Fractional Programming (LFP) problems. A comparative study is also made on different duals of LP & LFP. We then develop an improved decomposition approach for showing the relationship of primal and dual approach of LP & LFP problems by giving algorithm. Numerical examples are given to demonstrate our method. A computer programming code is also developed for showing primal and dual decomposition approach of LP & LFP with proper instructions using AMPL. Finally, we have drawn a conclusion stating the privilege of our method of computation.
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.
In this paper, we improve a combined algorithm and develop a uniform computer technique for solving constrained, unconstrained Non Linear Programming (NLP) and Quadratic Programming (QP) problems into a single framework. For this, we first review the basic algorithms of convex and concave QP as well as general NLP problems. We also focus on the development of the graphical representations. We use MATHEMATICA 9.0 to develop this algorithmic technique. We present a number of numerical examples to demonstrate our method.
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