| PIECEWISE LINEAR NCP FUNCTION FOR QP FREE FEASIBLE METHOD |
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| 引用本文： | Pu Dingguo Zhou Yan. PIECEWISE LINEAR NCP FUNCTION FOR QP FREE FEASIBLE METHOD[J]. 高校应用数学学报(英文版), 2006, 21(3): 289-301. DOI: 10.1007/s11766-003-0005-6 |
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| 作者姓名： | Pu Dingguo Zhou Yan |
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| 作者单位： | [1]Department of Applied Mathematics, Tongji University, Shanghai, 200092, China. [2]Department of Management Science and Engineering, Qingdao University, Qingdao, 266071, China. |
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| 基金项目： | the Natural Science Foundation of China （10371089, 10571137）. |
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| 摘 要： | In this paper,a QP-free feasible method with piecewise NCP functions is proposed for nonlinear inequality constrained optimization problems.The new NCP functions are piece- wise linear-rational,regular pseudo-smooth and have nice properties.This method is based on the solutions of linear systems of equation reformulation of KKT optimality conditions,by using the piecewise NCP functions.This method is implementable and globally convergent without assuming the strict complementarity condition,the isolatedness of accumulation points.Fur- thermore,the gradients of active constraints are not requested to be linearly independent.The submatrix which may be obtained by quasi-Newton methods,is not requested to be uniformly positive definite.Preliminary numerical results indicate that this new QP-free method is quite promising.
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| 关 键 词： | 拘泥最优化 半光滑性 非线性互补 收敛 |
| 收稿时间： | 2005-10-20 |
Piecewise linear NCP function for QP free feasible method |
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| Pu Dingguo,Zhou Yan. Piecewise linear NCP function for QP free feasible method[J]. Applied Mathematics A Journal of Chinese Universities, 2006, 21(3): 289-301. DOI: 10.1007/s11766-003-0005-6 |
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| Authors: | Pu Dingguo Zhou Yan |
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| Affiliation: | (1) Department of Applied Mathematics, Tongji University, 200092 Shanghai, China;(2) Department of Management Science and Engineering, Qingdao University, 266071 Qingdao, China |
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| Abstract: | In this paper, a QP-free feasible method with piecewise NCP functions is proposed for nonlinear inequality constrained optimization problems. The new NCP functions are piecewise linear-rational, regular pseudo-smooth and have nice properties. This method is based on the solutions of linear systems of equation reformulation of KKT optimality conditions, by using the piecewise NCP functions. This method is implementable and globally convergent without assuming the strict complementarity condition, the isolatedness of accumulation points. Purr thermore, the gradients of active constraints are not requested to be linearly independent. The submatrix which may be obtained by quasi-Newton methods, is not requested to be uniformly positive definite. Preliminary numerical results indicate that this new QP-free method is quite promising. |
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| Keywords: | constrained optimization semismooth nonlinear complementarity convergence. |
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