广义凸区间值优化问题的最优性条件

doi:10.15960/j.cnki.issn.1007-6093.2020.04.002

Abstract

Abstract: A new interval CW-order relation is introduced in this paper. By the CW-order relation, the interval valued pre-invex, pseudo-invex and quasi-invex functions are introduced, then we established the relationships among these kinds of functions. Finally, under the interval value invexity, the optimal condition of the interval valued optimization problem is established by using the scalarization method.

Key words: generalized convexity, interval value optimization problem, interval valued function, optimality condition

CLC Number:

O221.2

LI Jun, CHEN Jiawei, DENG Guangju. Optimality conditions of generalized convex interval valued optimization problems[J]. Operations Research Transactions, 2020, 24(4): 25-38.

References

[1] Wu H C. The Karush-Kuhn-Tucher optimality conditions in an optimization problem with interval-valued objective function[J]. European Journal of Operational Research, 2007, 176(1):46-59.
[2] Wu H C. The Karush-Kuhn-Tucher optimality conditions in multiobjective programming problems with interval-valued objective functions[J]. Fuzzy Optimization & Decision Making, 2009, 196(1):49-60.
[3] Wu H C. Duality theory for optimization problems with interval-valued objective functions[J]. Journal of Optimization Theory & Applications, 2010, 144(3):615-628.
[4] Jayswal A, Stancu-Minasian I, Ahmad I. On sufficiency and duality for a class of interval-valued programming problems[J]. Applied Mathematics & Computation, 2011, 218(8):4119-4127.
[5] 张建科. 广义凸不确定规划的最优性与对偶性[D]. 西安:西安电子科技大学, 2012.
[6] Ishibuchi H, Tanaka H. Multiobjective programming in optimization of the interval objective function[J]. European Journal of Operational Research, 1990, 48(2):219-225.
[7] Pini, Rita. Invexity and generalized convexity[J]. Optimization, 1991, 22(4):513-525.
[8] 宋士吉, 张玉利, 贾庆山. 非线性规划(第二版)[M]. 北京:清华大学出版社, 2013.
[9] Ben-Israel, Mond B. What is invexity?[J]. Journal of Australian Mathematical Society, 1986, 29:1-9.
[10] Kuhn H W, Tucher A W. Nonlinear programming[C]//Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, Berkeley:University of California Press, 1950, 81-492.
[11] 杨新民, 戎卫东. 广义凸性及其应用[M]. 北京:科学出版社, 2016.
[12] 彭再云, 李科科, 范琳煊. 向量值D-E-预不变真拟凸映射研究[J]. 系统科学与数学, 2016, 36(8):1298-1307.
[13] Peng Z Y, Wang Z Y, Lin Z, et al. A class of e-α-prequasiinvexity and mathematical programming[J]. Journal of Chongqing Normal University (Natural Science), 2018, 35(3):9-16.
[14] Peng Z Y, Chang S S. Some properties of semi-G-preinvex function[J]. Taiwanese Journal of Mathematics, 2013, 17(3):873-884.

Optimality conditions of generalized convex interval valued optimization problems

PDF

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 8

Recommended Articles

Metrics

Comments

[1]	CHEN Ruiting, XU Zhihui, GAO Ying. The optimality conditions of approximate solutions for quasiconvex multiobjective optimization problem [J]. Operations Research Transactions, 2019, 23(1): 35-44.
[2]	CHEN Lin, YANG Xinmin. Optimality conditions for a class of stochastic optimization problems with probabilistic complementarity constraints [J]. Operations Research Transactions, 2017, 21(2): 24-30.
[3]	YE Min, WU Zhiyou, ZHANG Liang. Necessary global optimality conditions and optimization methods for cubic polynomial optimization problems with linear constraints [J]. Operations Research Transactions, 2015, 19(2): 15-28.
[4]	ZHANG Liang,WANG Yan,LI Guoquan. Global optimality conditions for non-convex cubic minimization problem with binary constraints [J]. Operations Research Transactions, 2015, 19(2): 83-90.
[5]	LI Lihua, GAO Yan, WANG Gexia. Non-smooth optimality conditions for a class of dynamic systems with variable structure [J]. Operations Research Transactions, 2013, 17(3): 65-72.
[6]	LI Jianling, XIE Qin, JIAN Jinbao. Review on constraint qualifications and optimality conditions for mathematical programs with equilibrium constraints [J]. Operations Research Transactions, 2013, 17(3): 73-85.
[7]	CHAO Miantao, JIAN Jinbao , LIANG Dongying. Convex function\| sub-b-convex set\| sub-b-convex function\| pseudo-sub-b-convex function\| optimality conditions [J]. Operations Research Transactions, 2012, 16(2): 1-8.
[8]	ZHANG Li-Li, LI Jian-Yu, LI Xing-Si. An Integral Optimality Condition for Global Optimization [J]. Operations Research Transactions, 2011, 15(1): 1-10.