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 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)

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 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 interior point-proximal method of multipliers for convex quadratic programming

2020 ◽  
Author(s):  
Spyridon Pougkakiotis ◽  
Jacek Gondzio
Keyword(s):  
Quadratic Programming ◽  
Interior Point ◽  
Interior Point Method ◽  
Polynomial Complexity ◽  
Convex Quadratic Programming ◽  
Method Of Multipliers ◽  
Penalty Parameter ◽  
Proximal Method ◽  
Quadratic Programming Problems ◽  
Primal Dual

Abstract In this paper we combine an infeasible Interior Point Method (IPM) with the Proximal Method of Multipliers (PMM). The resulting algorithm (IP-PMM) is interpreted as a primal-dual regularized IPM, suitable for solving linearly constrained convex quadratic programming problems. We apply few iterations of the interior point method to each sub-problem of the proximal method of multipliers. Once a satisfactory solution of the PMM sub-problem is found, we update the PMM parameters, form a new IPM neighbourhood and repeat this process. Given this framework, we prove polynomial complexity of the algorithm, under standard assumptions. To our knowledge, this is the first polynomial complexity result for a primal-dual regularized IPM. The algorithm is guided by the use of a single penalty parameter; that of the logarithmic barrier. In other words, we show that IP-PMM inherits the polynomial complexity of IPMs, as well as the strict convexity of the PMM sub-problems. The updates of the penalty parameter are controlled by IPM, and hence are well-tuned, and do not depend on the problem solved. Furthermore, we study the behavior of the method when it is applied to an infeasible problem, and identify a necessary condition for infeasibility. The latter is used to construct an infeasibility detection mechanism. Subsequently, we provide a robust implementation of the presented algorithm and test it over a set of small to large scale linear and convex quadratic programming problems. The numerical results demonstrate the benefits of using regularization in IPMs as well as the reliability of the 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.

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