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

2016 ◽  
Vol 35 ◽  
pp. 41-55
Author(s):  
HK Das ◽  
M Babul Hasan
Keyword(s):  
Linear Programming ◽  
Quadratic Programming ◽  
Graphical Representations ◽  
Computer Technique ◽  
Numerical Examples ◽  
Non Linear Programming ◽  
Non Linear ◽  
Quadratic Programming Problems ◽  
Algorithmic Technique ◽  
Combined Algorithm

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.GANIT J. Bangladesh Math. Soc.Vol. 35 (2015) 41-55

Decomposition Procedure for Solving NLP and QP Problems based on Lagrange and Sander's Method

2016 ◽  
Vol 7 (4) ◽  
pp. 67-93
Author(s):  
H. K. Das
Keyword(s):  
Linear Programming ◽  
Optimal Solution ◽  
Computational Technique ◽  
Lagrange Method ◽  
Computer Technique ◽  
Numerical Examples ◽  
Non Linear Programming ◽  
Decomposition Procedure ◽  
Concave Quadratic Programming ◽  
Modified Algorithm

This paper develops a decompose procedure for finding the optimal solution of convex and concave Quadratic Programming (QP) problems together with general Non-linear Programming (NLP) problems. The paper also develops a sophisticated computer technique corresponding to the author's algorithm using programming language MATHEMATICA. As for auxiliary by making comparison, the author introduces a computer-oriented technique of the traditional Karush-Kuhn-Tucker (KKT) method and Lagrange method for solving NLP problems. He then modify the Sander's algorithm and develop a new computational technique to evaluate the performance of the Sander's algorithm for solving NLP problems. The author observe that the technique avoids some certain numerical difficulties in NLP and QP. He illustrates a number of numerical examples to demonstrate his method and the modified algorithm.

scholarly journals A Technique for Solving Special Type Quadratic Programming Problems

2012 ◽  
Vol 60 (2) ◽  
pp. 209-215
Author(s):  
M. Babul Hasan
Keyword(s):  
Quadratic Programming ◽  
Simplex Method ◽  
Linear Functions ◽  
Hospital Planning ◽  
Basic Variable ◽  
Computer Technique ◽  
Corporate Planning ◽  
Numerical Examples ◽  
Considerable Research ◽  
Quadratic Programming Problems

Because of its usefulness in production planning, financial and corporate planning, health care and hospital planning, quadratic programming (QP) problems have attracted considerable research and interest in recent years. In this paper, we first extend the simplex method for solving QP problems by replacing one basic variable at an iteration of simplex method. We then develop an algorithm and a computer technique for solving quadratic programming problem involving the product of two indefinite factorized linear functions. For developing the technique, we use programming language MATHEMATICA. We also illustrate numerical examples to demonstrate our technique.DOI: http://dx.doi.org/10.3329/dujs.v60i2.11520 Dhaka Univ. J. Sci. 60(2): 209-215, 2012 (July)

scholarly journals A comparative study of the methods of solving non-linear programming problem

1970 ◽  
Vol 4 (1) ◽  
pp. 28-34
Author(s):  
Bimal Chandra Das
Keyword(s):  
Linear Programming ◽  
Quadratic Programming ◽  
Comparative Study ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Feasible Region ◽  
Non Linear Programming ◽  
Condition Method ◽  
Non Linear ◽  
Matlab Programming

The work present in this paper is based on a comparative study of the methods of solving Non-linear programming (NLP) problem. We know that Kuhn-Tucker condition method is an efficient method of solving Non-linear programming problem. By using Kuhn-Tucker conditions the quadratic programming (QP) problem reduced to form of Linear programming(LP) problem, so practically simplex type algorithm can be used to solve the quadratic programming problem (Wolfe's Algorithm).We have arranged the materials of this paper in following way. Fist we discuss about non-linear programming problems. In second step we discuss Kuhn- Tucker condition method of solving NLP problems. Finally we compare the solution obtained by Kuhn- Tucker condition method with other methods. For problem so consider we use MATLAB programming to graph the constraints for obtaining feasible region. Also we plot the objective functions for determining optimum points and compare the solution thus obtained with exact solutions. Keywords: Non-linear programming, objective function ,convex-region, pivotal element, optimal solution. DOI: 10.3329/diujst.v4i1.4352 Daffodil International University Journal of Science and Technology Vol.4(1) 2009 pp.28-34

scholarly journals TRANSFORMASI LINIER UNTUK PERSOALAN PROGRAM KUADRATIK NOL-SATU

2017 ◽  
Vol 3 (2) ◽  
Author(s):  
M Khahfi Zuhanda
Keyword(s):  
Linear Programming ◽  
Quadratic Programming ◽  
Objective Function ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Interesting Issue ◽  
Non Linear Programming ◽  
Quadratic Equations ◽  
Non Linear ◽  
Special Case

Program non linier merupakan persoalan yang cukup menarik untuk di bahas oleh matematikawan. Salah satunya program kuadratik nol-satu yang fungsi tujuan dan kendala berbentuk persamaan kuadratik. Program kuadratik nol-satu merupakan kelas khusus dalam pemrograman non-linier karena persyaratan peubah keputusan bernilai nol-satu. Tulisan ini akan mengajukan sebuah teknik untuk menyelesaikan persoalan program kuadratik nol-satu yang dikembangkan oleh Sherali dan Smith. Teknik ini mengubah Quadratic Problems (QP) menjadi kebentuk Bilinier Problems(BP) terlebih dahulu. Akhir dari proses ini mengakibatkan transformasi  program kuadratik nol-satu menjadi persoalan linier nol-satu. Kata Kunci :  integer, linierisasi, nol-satu, program kuadratik  ABSTRACT Non-linear programming is an interesting issue to be discussed by mathematician. One of them is a zero-one quadratic programming, where the objective function and constraints are quadratic equations. The zero-one quadratic programming is a special case in non-linear programming because of the requirement of value variable is zero-one. This paper propose a technique for solving the zero-one quadratic programming problem was developed by Sherali and Smith. This technique converts the Quadratic Problems (QP) into Bilinier Problems (BP) first. The end of this process will transfrom zero-one quadratic programming to zero-one linear programming problem Keywords: Integer, Linearization, Quadratic Programming, Zero-One, 

scholarly journals Application of Non-Linear Programming to Portfolio Management on some Insurance Companies (AIICO,LINKAGE, NIGER, Mutual benefit and LASACO) using Return on Asset

2020 ◽  
Vol 4 (7) ◽  
pp. 1-7
Author(s):  
Olawale Kolapo Steve Emiola ◽  
Musibau Abayomi Omoloye ◽  
Christiana Uchechukwu Arinze
Keyword(s):  
Linear Programming ◽  
Quadratic Programming ◽  
Programming Problem ◽  
Portfolio Management ◽  
Linear Programming Problem ◽  
Insurance Companies ◽  
Insurance Company ◽  
Mutual Benefit ◽  
Non Linear Programming ◽  
Non Linear

This study investigate non-linear programming problem that is, quadratic programming and its application to portfolio management. The data of return on asset of five different insurance companies namely: AIICO, LINKAGE, NIGER, MUTUAL BENEFIT, and LASACO insurance company was collected and a model was fixed. These data were analyzed using quadratic programming in conjunction with LINGO software. The result of the analyzed data revealed that the allocation of fund for each insurance companies should be done with the same percent for LINKAGE, NIGER, MUTUAL BENEFIT and other percent to AIICO insurance company respectively with increment of 24% on return.

scholarly journals A Procedure for Solving Quadratic Programming Problems

2017 ◽  
Vol 65 (1) ◽  
pp. 9-13
Author(s):  
HK Das
Keyword(s):  
Linear Programming ◽  
Quadratic Programming ◽  
Computer Technique ◽  
Quadratic Programming Problems ◽  
General Computer

In this paper, we study on the well-known procedure of quadratic programming (QP) and its corresponding linear programming (LP) problem. We then introduce a LP problem corresponding to the QP problem. Unfortunately, an unboundedness question arises into the new converting LP problem. We then modify the converted LP problem that overcomes the unboundedness. We introduce a general computer technique that can be solved the QP problem. An example is given to clarify the procedure and the computer technique. Dhaka Univ. J. Sci. 65(1): 9-13, 2017 (January)

scholarly journals A Proposed Technique for Solving Quasi-Concave Quadratic Programming Problems with Bounded Variables by Objective Separable Method

2016 ◽  
Vol 64 (1) ◽  
pp. 51-58
Author(s):  
M Asadujjaman ◽  
M Babul Hasan
Keyword(s):  
Linear Programming ◽  
Quadratic Programming ◽  
Objective Function ◽  
Programming Language ◽  
Optimal Solution ◽  
Linear Functions ◽  
Numerical Examples ◽  
Bounded Variables ◽  
Quadratic Programming Problems ◽  
Concave Quadratic Programming

In this paper, a new method namely, objective separable method based on Linear Programming with Bounded Variables Algorithm is proposed for finding an optimal solution to a Quasi-Concave Quadratic Programming Problems with Bounded Variables in which the objective function involves the product of two indefinite factorized linear functions and the constraint functions are in the form of linear inequalities. For developing this method, we use programming language MATHEMATICA. We also illustrate numerical examples to demonstrate our method.Dhaka Univ. J. Sci. 64(1): 51-58, 2016 (January)

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