A polynomial algorithm for the quadratic programming problem

2014 ◽  
Vol 29 (3) ◽  
Author(s):  
Valentin A. Bereznev
Keyword(s):  
Computational Complexity ◽  
Quadratic Form ◽  
Quadratic Programming ◽  
Programming Problem ◽  
Polynomial Complexity ◽  
Polynomial Algorithm ◽  
Positive Definite Matrix ◽  
Positive Definite ◽  
Quadratic Programming Problem ◽  
Convex Polyhedral Cone

AbstractAn approach based on projection of a vector onto a pointed convex polyhedral cone is proposed for solving the quadratic programming problem with a positive definite matrix of the quadratic form. It is proved that this method has polynomial complexity. A method is said to be of polynomial computational complexity if the solution to the problem can be obtained in N

A Parallel Dual Projection Algorithm for Solving Positive Definite Quadratic Programming Problems

1990 ◽  
Author(s):  
Yugang Wang ◽  
Eric Sandgren
Keyword(s):  
Quadratic Programming ◽  
Positive Definite ◽  
Parallel Computer ◽  
Projection Algorithm ◽  
Test Problems ◽  
Local Optimum ◽  
Active Constraint ◽  
Search Point ◽  
Quadratic Programming Problems ◽  
Dual Projection

Abstract Two parallel algorithms, a dual projection algorithm and a hybrid dual projection algorithm, are proposed for solving positive definite quadratic programming problems. In each iteration of the algorithms, the search point is always a local optimum point on the current active constraint basis for both adding and dropping constraint operations. The advantage of this strategy is that the computation is stable and all operations maintain parallel properties. Only a pseudo-inverse matrix must be updated instead of two matrices in Goldfarb’s dual algorithm in a basis change. Both computational and space complexities are reduced by about half. When the search point reaches a vertex in the dual space, a pivot operation is employed to update the basis in the hybrid dual projection algorithm in place of the addition and deletion operations in the dual projection algorithm. This reduces the computational complexity by half in future iterations. Some suggestions are presented to further enhance the computational speed of the algorithm. Numerical results are presented based on randomly generated test problems. Comparison with other methods demonstrates that the new algorithm is efficient and stable and points to the possibility of implementation on a parallel computer.

scholarly journals Optimal solution approximation for infinite positive-definite quadratic programming

1995 ◽  
Vol 85 (2) ◽  
pp. 235-248 ◽  
Author(s):  
P. Benson ◽  
R. L. Smith ◽  
I. E. Schochetman ◽  
J. C. Bean
Keyword(s):  
Quadratic Programming ◽  
Optimal Solution ◽  
Positive Definite
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