Study of Semistrict-G-E-Semipreinvex Functions and Applications in Nonlinear Programming

PENG Zai-yun; SUN Jia-hui; LI Ke-ke; ZHANG Shi-sheng

doi:10.21656/1000-0887.370280

Volume 38 Issue 7

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Article Navigation > Applied Mathematics and Mechanics > 2017 > 38(7): 827-836

PENG Zai-yun, SUN Jia-hui, LI Ke-ke, ZHANG Shi-sheng. Study of Semistrict-G-E-Semipreinvex Functions and Applications in Nonlinear Programming[J]. Applied Mathematics and Mechanics, 2017, 38(7): 827-836. doi: 10.21656/1000-0887.370280

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Study of Semistrict-G-E-Semipreinvex Functions and Applications in Nonlinear Programming

doi: 10.21656/1000-0887.370280

¹College of Mathematics and Statistics, Chongqing Jiaotong University, Chongqing 400074, P.R.China;²School of Management, Xi’an Polytechnic University, Xi’an 710048, P.R.China;³School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, P.R.China;⁴School of Statistics and Mathematics,Yunnan University of Finance and Economics, Kunming 650224, P.R.China

Funds: The National Natural Science Foundation of China(11471059;11431004); China Postdoctoral Science Foundation(2015M580774;2016T90837)

Received Date: 2016-09-13
Rev Recd Date: 2017-05-10
Publish Date: 2017-07-15

Abstract

Abstract

A new class of generalized convex functions, namely the semistrict-G-E-semipreinvex functions were proposed, which are a class of very important generalized convex functions and make a true generalization of both the semistrict-G-semipreinvex functions and the semistrict-E-preinvex functions. Firstly, several examples were given to illustrate the existence of semistrict-G-E-semipreinvex functions and the dependence on the related generalized convex functions. Afterwards, the basic characteristics of the semistrict-G-E-semipreinvex functions were discussed. Finally, some applications of the semistrict-G-E-semipreinvex functions in nonlinear programming problems without constraint and with inequality constraints were studied respectively, and some optimality results were obtained; moreover, some examples were given to illustrate the correctness of the obtained results.
- E-semi-connected set,
- semistrict-G-E-semipreinvex function,
- characteristics,
- nonlinear programming,
- application

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References

[1]	Hanson M A. On sufficiency of the Kuhn-Tucker conditions[J]. Journal of Mathematical Analysis and Applications,1981,80(2): 545-550.
[2]	Weir T, Mond B. Pre-invex functions in multiple objective optimization[J]. Journal of Mathematical Analysis and Applications,1988,136(1): 29-38.
[3]	YANG Xin-min, LI Duan. On properties of preinvex functions[J]. Journal of Mathematical Analysis and Applications,2001,256(1): 229-241.
[4]	YANG Xin-min, LI Duan. Semistrictly preinvex functions[J]. Journal of Mathematical Analysis and Applications,2001,258(1): 287-308.
[5]	Yang X Q, CHEN Guang-ya. A class of nonconvex functions and pre-variational inequalities[J]. Journal of Mathematical Analysis and Applications,1992,169(2): 359-373.
[6]	颜丽佳, 刘芙萍. 强预不变凸函数[J]. 重庆师范大学学报(自然科学版), 2005,22(1):11-15.(YAN Li-jia, LIU Fu-ping. Strongly preinvex functions[J]. Journal of Chongqing Normal University (Natural Science Edition),2005,22(1): 11-15.(in Chinese))
[7]	彭再云, 李永红. 半严格-G-半预不变凸性与最优化[J]. 应用数学和力学, 2013,34(8): 836-845.(PENG Zai-yun, LI Yong-hong. Semistrict-G-semi-preinvexity and optimization[J]. Applied Mathematics and Mechanics,2013,34(8): 836-845.(in Chinese))
[8]	李科科, 彭再云, 万轩, 等. 严格 G -半预不变凸性及其应用[J]. 重庆师范大学学报(自然科学版), 2015,32(6): 1-8.(LI Ke-ke, PENG Zai-yun, WAN Xuan, et al. The study of strict G -semi-preinvexity and its applications[J]. Journal of Chongqing Normal University (Natural Science),2015,32(6): 1-8.(in Chinese))
[9]	彭再云, 秦南南, 李科科.G-E-半预不变凸型多目标规划的 Wolfe 型对偶[J]. 应用数学学报, 2015,38(6): 1103-1114.(PENG Zai-yun, QIN Nan-nan, LI Ke-ke. Wolf type duality of G-E-semi-preinvex type multiobjective programming problems[J]. Acta Mathematicae Applicatae Sinica,2015,38(6): 1103-1114.(in Chinese))
[10]	Fulga C, Preda V. Nonlinear programming with E -preinvex and local E -preinvex functions[J]. European Journal of Operational Research,2009,192(2): 737-743.
[11]	彭再云, 周选林, 赵勇. 强G-预不变凸函数的性质及应用[J]. 重庆师范大学学报(自然科学版), 2012,29(4):12-17.(PENG Zai-yun, ZHOU Xuan-lin, ZHAO Yong. Characteristics and applications of strongly G-preinvex functions[J]. Journal of Chongqing Normal University (Natural Science), 2012,29(4): 12-17.(in Chinese))
[12]	彭再云, 李科科, 张石生. 向量 D-η-Ｅ半预不变凸映射与向量优化[J]. 应用数学和力学, 2014,35(9): 1020-1032.(PENG Zai-yun, LI Ke-ke, ZHANG Shi-sheng. Semipreinvex vector mappings and vector optimization[J]. Applied Mathematics and Mechanics,2014,35(9): 1020-1032.(in Chinese))
[13]	赵映雪. 一类广义凸性及其在最优化理论中的应用[D]. 硕士学位论文. 金华: 浙江师范大学, 2005.(ZHAO Ying-xue. A type of generalized convexity and applications in optimization theory[D]. Master Thesis. Jinhua: Zhejiang Normal University, 2005.(in chinese))
[14]	唐莉萍, 杨新民. 关于D-半预不变凸性的某些新性质[J]. 应用数学和力学, 2015,36(3): 325-331.(TANG Li-ping, YANG Xin-min. A note on some new characteristics of D-semi-preinvexity[J]. Applied Mathematics and Mechanics,2015,36(3): 325-331.(in Chinese))