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)

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)

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 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 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

scholarly journals A Proposed Technique for Solving Linear Fractional Bounded Variable Problems

2012 ◽  
Vol 60 (2) ◽  
pp. 223-230
Author(s):  
H.K. Das ◽  
M. Babul Hasan
Keyword(s):  
Linear Programming ◽  
Objective Function ◽  
Programming Language ◽  
Simplex Algorithm ◽  
Computational Effort ◽  
New Method ◽  
Bounded Variables ◽  
Primal Dual ◽  
Dual Simplex ◽  
Dual Simplex Algorithm

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) 

scholarly journals A New Approach to Find an Optimal Solution of a Fuzzy Linear Programming Problem by Fuzzy Dynamic Programming

2018 ◽  
Vol 7 (4.10) ◽  
pp. 360
Author(s):  
T. Nagalakshmi ◽  
G. Uthra
Keyword(s):  
Dynamic Programming ◽  
Linear Programming ◽  
Objective Function ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Optimal Solution ◽  
Fuzzy Linear Programming ◽  
New Approach ◽  
The Cost ◽  
Recursive Equations

This paper mainly focuses on a new approach to find an optimal solution of a fuzzy linear programming problem with the help of Fuzzy Dynamic Programming. Linear programming deals with the optimization of a function of variables called an objective function, subject to a set of linear inequalities called constraints. The objective function may be maximizing the profit or minimizing the cost or any other measure of effectiveness subject to constraints imposed by supply, demand, storage capacity, etc., Moreover, it is known that fuzziness prevails in all fields. Hence, a general linear programming problem with fuzzy parameters is considered where the variables are taken as Triangular Fuzzy Numbers. The solution is obtained by the method of FDP by framing fuzzy forward and fuzzy backward recursive equations. It is observed that the solutions obtained by both the equations are the same. This approach is illustrated with a numerical example. This feature of the proposed approach eliminates the imprecision and fuzziness in LPP models. The application of Fuzzy set theory in the field of dynamic Programming is called Fuzzy Dynamic Programming. 

The Improvement of Optimality Test over Possible Reaction Set in Bilevel Linear Optimization with Ambiguous Objective Function of the Follower

2015 ◽  
Vol 19 (5) ◽  
pp. 645-654 ◽  
Author(s):  
Puchit Sariddichainunta ◽  
◽  
Masahiro Inuiguchi
Keyword(s):  
Linear Programming ◽  
Objective Function ◽  
Linear Optimization ◽  
Convex Polytope ◽  
Optimal Solution ◽  
Global Optimality ◽  
Basic Solution ◽  
Bilevel Linear Programming ◽  
Coefficient Vector ◽  
Optimality Test

Verifying a rational response is the most crucial step in searching for an optimal solution in bilevel linear programming. Such verification is even difficult in a model with ambiguous objective function of the follower who reacts rationally to a leader’s decision. In our model, we assume that the ambiguous coefficient vector of follower lies in a convex polytope and we formulate bilevel linear programming with the ambiguous objective function of the follower as a special three-level programming problem. We use thek-th best method that sequentially enumerates a solution and examine whether it is the best of all possible reactions. The optimality test process over possible reactions in lower-level problems usually encounters degenerate bases that become obstacles to verifying the optimality of an enumerated solution efficiently. To accelerate optimality verification, we propose search strategies and the evaluation of basic possible reactions adjacent to a degenerate basic solution. We introduce these methods in both local and global optimality testing, confirming the effectiveness of our proposed methods in numerical experiments.

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.

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