| ON ALTERNATIVE OPTIMAL SOLUTIONS TO QUASIMONOTONIC PROGRAMMING WITH LINEAR CONSTRAINTS |
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| 作者姓名： | Xue Shengjia |
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| 作者单位： | School of Management, Jinan University, Guangzhou 510632, China. |
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| 基金项目： | 济南大学研究基金会资助项目 |
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| 摘 要： | In this paper, the nonlinear programming problem with quasimonotonic （ both quasiconvex and quasiconcave ）objective function and linear constraints is considered. With the decomposition theorem of polyhedral sets, the structure of optimal solution set for the programming problem is depicted. Based on a simplified version of the convex simplex method, the uniqueness condition of optimal solution and the computational procedures to determine all optimal solutions are given, if the uniqueness condition is not satisfied. An illustrative example is also presented.
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| 关 键 词： | 准单调规划 线性约束 择一最优解 多面体集 |
| 收稿时间： | 2006-04-30 |
On alternative optimal solutions to quasimonotonic programming with linear constraints |
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| Xue Shengjia.ON ALTERNATIVE OPTIMAL SOLUTIONS TO QUASIMONOTONIC PROGRAMMING WITH LINEAR CONSTRAINTS[J].Applied Mathematics A Journal of Chinese Universities,2007,22(1):119-125. |
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| Authors: | Xue Shengjia |
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| Institution: | (1) School of Management, Jinan University, Guangzhou, 510632, China |
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| Abstract: | In this paper, the nonlinear programming problem with quasimonotonic ( both quasiconvex and quasiconcave )objective function and linear constraints is considered. With the decomposition theorem of polyhedral sets, the structure of optimal solution set for the programming problem is depicted. Based on a simplified version of the convex simplex method,the uniqueness condition of optimal solution and the computational procedures to determine all optimal solutions are given, if the uniqueness condition is not satisfied. An illustrative example is also presented. |
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| Keywords: | quasimonotonic programming problem polyhedral set decomposition theorem alternative optimal solution convex simplex method |
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