A Barrier Function Method for the Nonconvex Quadratic Programming Problem with Box Constraints |
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Authors: | Chuangyin Dang Lei Xu |
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Institution: | (1) Department of Manufacturing Engineering and Engineering Management, City University of Hong Kong, Kowloon, Hong Kong;(2) Department of Computer Science and Engineering, Chinese University of Hong Kong, New Territories, Hong Kong |
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Abstract: | In this paper a barrier function method is proposed for approximating a solution of the nonconvex quadratic programming problem with box constraints. The method attempts to produce a solution of good quality by following a path as the barrier parameter decreases from a sufficiently large positive number. For a given value of the barrier parameter, the method searches for a minimum point of the barrier function in a descent direction, which has a desired property that the box constraints are always satisfied automatically if the step length is a number between zero and one. When all the diagonal entries of the objective function are negative, the method converges to at least a local minimum point of the problem if it yields a local minimum point of the barrier function for a sequence of decreasing values of the barrier parameter with zero limit. Numerical results show that the method always generates a global or near global minimum point as the barrier parameter decreases at a sufficiently slow pace. |
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Keywords: | Nonconvex Quadratic Programming Box Constraints Global Optimization Barrier Function Descent Direction Iterative Method |
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