引用本文:王子元, 王泾晶, 彭再云, 邵重阳, 周大琼.E-拟α-预不变型凸函数与最优化[J].西南大学学报(自然科学版),2019,41(9):77~86
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E-拟α-预不变型凸函数与最优化
王子元, 王泾晶, 彭再云, 邵重阳, 周大琼1,2
1. 重庆交通大学 数学与统计学院, 重庆 400074;2.
2. 英属哥伦比亚大学 数学系, 加拿大 英属哥伦比亚省 基隆拿 V1V1V7
摘要:
研究了E-拟α-预不变型凸函数的性质与应用.首先,给出了E-拟α-预不变凸函数的定义,用例子说明了其存在性,并给出了在条件A与条件B下(半)严格E-拟α-预不变凸函数的等价刻画.其次,提出了E-拟α-预不变凸条件下的一类约束优化问题(NP1),证明了问题(NP1)可行解集、最优解集的E-α-不变凸性,并给出了问题(NP1)局部最优解的性质.最后,讨论了E-α-预不变凸函数的性质,给出了该类函数的等价刻画,获得了不等式约束下E-α-预不变凸多目标规划问题(MOP1)的最优性结果,并举例验证了所得结论的正确性.
关键词:  E-拟α-预不变凸函数  非线性规划问题  最优性条件  E-α-预不变凸函数
DOI:10.13718/j.cnki.xdzk.2019.09.010
分类号:O221.2
基金项目:重庆市自然科学基金资助项目(cstc2018jcyjAX0337);重庆市创新团队资助项目(CXTDX201601022);重庆交通大学研究生教育创新基金项目(2019S0123);最优化与控制重庆市重点实验室开放课题(CSSXKFKTZ201801);重庆市巴渝学者计划资助项目.
E-α-prequasiinvex-Type Functions and Their Optimization
WANG Zi-yuan, WANG Jing-jing, PENG Zai-yun, SHAO Chong-yang, ZHOU Da-qiong1,2
1. College of Mathematics and Statistics, Chongqing Jiaotong University, Chongqing 400074, China;2.
2. Department of Mathematics, University of British Columbia, Kelowna, BC V1 V1 V7, Canada
Abstract:
In this paper, we mainly study the concept of E-α-prequasiinvex-type functions and their applications. First, the definition of E-α-prequasiinvex functions is given, with examples demonstrating their existence. The necessary and sufficient conditions of strictly (semi-strictly) E-α-prequasiinvex functions under the assumption of Condition A and Condition B are discussed. Then, the nonlinear programming problem (NP1) with inequality constraints under the E-α-prequasiinvex condition is proposed. The E-α-invexity of the feasible solution set and optimal solution set of (NP1) is proved, and the property of the local optimal solution of NP1 is given. Finally, the concepts of E-α-preinvex functions are discussed, the equivalent characterization of E-α-preinvex functions is given, and the optimal result of the multi-objective programming problem under E-α-preinvex condition is obtained. Examples are given to verify the conclusions reached.
Key words:  E-α-prequasiinvex function  nonlinear programming problem  optimal criterion  E-α-preinvex function
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