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| 摘要: |
| 本文研究了多目标优化问题的(ε,ε)-拟近似解.利用文献[1]给出的多目标优化问题统一的非线性标量化问题,在没有任何凸性条件下,研究了多目标优化问题的(ε,ε)-拟近似解的充分和必要条件.最后,利用文献[2]中给出的的范数,对多目标优化问题的(ε,ε)-拟近似解进行了非线性标量化刻画.本文第3节推广了文献[1]中的结果. |
| 关键词: 多目标优化 拟近似解 标量化 |
| DOI： |
| 分类号:O221.6 |
| 基金项目:国家自然科学基金(11201511);重庆市重点实验室专项项目(CSTC,2011KLORSE03);重庆市科委项目(cstc2015jcyjA00005);重庆市教委项目(KJ1500309). |
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| NONLINEAR SCALARIZATIONS FOR (ε,ε)-APPROXIMATE QUASI SOLUTIONS OF MULTIOBJECTIVE OPTIMIZATION PROBLEMS |
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YUE Rui-xue,GAO Ying
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| Abstract: |
| In this paper, we consider (ε,ε)-approximate quasi e-cient solutions of multiobjective optimization problems. Based on the uniform nonlinear scalarization problems given in [1], we derive several necessary and sufficient conditions for (ε,ε)-approximate quasi e-cient solutions of multiobjective optimization problems without any convexity conditions. Finally, using the norm given in the [2], we derive a kind of nonlinear scalarization problem for (ε,ε)-approximate quasi e-cient solutions of multiobjective optimization problems. Section 3 in this paper extends the results in [1]. |
| Key words: multiobjective optimization approximate quasi solutions scalarization |
