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 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

A Proposed Technique for Solving Quasi-Concave Quadratic Programming Problems with Bounded Variables

2015 ◽  
Vol 63 (2) ◽  
pp. 111-117
Author(s):  
M Asadujjaman ◽  
M Babul Hasan
Keyword(s):  
Quadratic Programming ◽  
Optimal Solution ◽  
Linear Functions ◽  
Dual Simplex Method ◽  
Numerical Examples ◽  
Bounded Variables ◽  
Quadratic Programming Problems ◽  
Primal Dual ◽  
Dual Simplex ◽  
Concave Quadratic Programming

In this paper, a new method is proposed for finding an optimal solution to a Quasi-Concave Quadratic Programming Problem with Bounded Variables in which the objective function involves the product of two indefinite factorized linear functions and constraints functions are in the form of linear inequalities. The proposed method is mainly based upon the primal dual simplex method. The Linear Programming with Bounded Variables (LPBV) algorithm is extended to solve quasi-concave Quadratic Programming with Bounded Variables (QPBV). For developing this method, we use programming language MATHEMATICA. We also illustrate numerical examples to demonstrate our method.Dhaka Univ. J. Sci. 63(2):111-117, 2015 (July)

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)

scholarly journals Optimality Conditions for Fuzzy Number Quadratic Programming with Fuzzy Coefficients

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Xue-Gang Zhou ◽  
Bing-Yuan Cao ◽  
Seyed Hadi Nasseri
Keyword(s):  
Quadratic Programming ◽  
Objective Function ◽  
Optimality Conditions ◽  
Fuzzy Number ◽  
Duality Theory ◽  
Quadratic Function ◽  
Linear Functions ◽  
Duality Results ◽  
Constraint Set ◽  
Quadratic Programming Problems

The purpose of the present paper is to investigate optimality conditions and duality theory in fuzzy number quadratic programming (FNQP) in which the objective function is fuzzy quadratic function with fuzzy number coefficients and the constraint set is fuzzy linear functions with fuzzy number coefficients. Firstly, the equivalent quadratic programming of FNQP is presented by utilizing a linear ranking function and the dual of fuzzy number quadratic programming primal problems is introduced. Secondly, we present optimality conditions for fuzzy number quadratic programming. We then prove several duality results for fuzzy number quadratic programming problems with fuzzy coefficients.

scholarly journals An Approach for Solving Linear Fractional Programming Problems

2012 ◽  
Vol 1 (4) ◽  
pp. 298 ◽  
Author(s):  
Andrew Oyakhobo Odior
Keyword(s):  
Fractional Programming ◽  
Hospital Planning ◽  
Linear Fractional Programming ◽  
Corporate Planning ◽  
New Approach ◽  
Considerable Research ◽  
Fractional Linear Programming ◽  
Linear Fractional Function ◽  
Partial Fractions ◽  
Fractional Function

Linear fractional programming problems are useful tools in production planning, financial and corporate planning, health care and hospital planning and as such have attracted considerable research interest. The paper presents a new approach for solving a fractional linear programming problem in which the objective function is a linear fractional function, while the constraint functions are in the form of linear inequalities. The approach adopted is based mainly upon solving the problem algebraically using the concept of duality and partial fractions and an example is given to clarify the developed method.

scholarly journals The PPADMM Method for Solving Quadratic Programming Problems

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 941
Author(s):  
Hai-Long Shen ◽  
Xu Tang
Keyword(s):  
Quadratic Programming ◽  
Alternating Direction Method ◽  
Equality Constraint ◽  
Matrix Analysis ◽  
Method Of Multipliers ◽  
Numerical Examples ◽  
Alternating Direction ◽  
Quadratic Programming Problems ◽  
Proximal Alternating Direction Method

In this paper, a preconditioned and proximal alternating direction method of multipliers (PPADMM) is established for iteratively solving the equality-constraint quadratic programming problems. Based on strictly matrix analysis, we prove that this method is asymptotically convergent. We also show the connection between this method with some existing methods, so it combines the advantages of the methods. Finally, the numerical examples show that the algorithm proposed is efficient, stable, and flexible for solving the quadratic programming problems with equality constraint.

scholarly journals A Computer Program for Solving LP Problems by 2-Basic Variables Replacement at Each Simplex Iteration

2013 ◽  
Vol 61 (1) ◽  
pp. 13-18
Author(s):  
M Babul Hasan ◽  
SM Asaduzzaman
Keyword(s):  
Linear Programming ◽  
Computer Program ◽  
Linear Programs ◽  
Basic Variable ◽  
Computer Technique ◽  
Numerical Examples ◽  
Replacement Method

In this paper, we develop a computer technique to implement the existing 2-basic variable replacement method of Paranjape for solving linear programming (LP) problems. To our knowledge there is no such computer oriented program which implemented Paranjape’s method. Our computer oriented program is a faster method for solving linear programs. A number of numerical examples are illustrated to demonstrate our algorithm. Dhaka Univ. J. Sci. 61(1): 13-18, 2013 (January) DOI: http://dx.doi.org/10.3329/dujs.v61i1.15090

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)

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