区间值映射的半连续性与凸性
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摘要
首先给出了区间数空间子集的有界性及确界等概念,并给出了确界的存在性定理;然后讨论了区间值映射的半连续性问题,给出了区间值映射的半连续性概念及相关性质;最后讨论了半连续区间值映射的凸性问题,给出了半连续区间值映射为凸区间值映射的两个充分条件.
First of all, it proves the concepts that subsets of interval number spaces have bound,supremum and infimum, meanwhile the existence theorems of supremum and infimum are given; Then we discuss the semi-continuity of interval value mapping and put forward its concept and related properties; Finally discuss the convexity of semi-continuous interval value mapping, and two sufficient conditions for semi-continuous interval value mapping to convex interval value mapping are given.
First of all, it proves the concepts that subsets of interval number spaces have bound,supremum and infimum, meanwhile the existence theorems of supremum and infimum are given; Then we discuss the semi-continuity of interval value mapping and put forward its concept and related properties; Finally discuss the convexity of semi-continuous interval value mapping, and two sufficient conditions for semi-continuous interval value mapping to convex interval value mapping are given.
引文
[1] Wu H C. The Karush-Kuhn-Tucker optimality conditions in multi-objective programming problems with interval-valued objective functions[J]. European Journal of Operational Research, 2009,196:49-60.
[2] Osuna-Gomez R, Chalco-Cano Y, Hernandez-Jimenez B, et al. Optimality conditions for generalized differentiable interval-valued functions[J]. Information Sciences, 2015,321:136-146.
[3] Chalco-Cano Y, Rufian-Lizan A, Roman-Flores H, et al. Calculus for interval-valued functions using generalized Hukuhara derivative and applications[J]. Fuzzy Sets and Systems, 2013,219:49-67.
[4] VanHoa N, Lupulescu V, RegandLe D. Solving interval-valued fractional initial value problems under Caputo gH-fractional differentiability[J]. Fuzzy Sets and Systems, 2017,309:1-34.
[5] Craven B D. Invex functions and constrained local minima[J]. Bull. Austral. Math. Soc., 1981,24(3):357-366.
[6] Zhang P. An interval mean-average absolute deviation model for multipored portfolio selection with risk control and cardinality constraints[J]. Soft Comput., 2016,20:1203-1212.
[7] Wu H C. On interval valued nonlinear programming problems[J]. Journal of Mathematical Analysis and Applications, 2008,338:299-316.
[8] Singh D, Dar B A, Kim D S. KKT optimality conditions in interval valued multi-objective programming with generalized differentiable functions[J]. European Journal of Operational Research,2016,254:29-39.
[9] Bao Y E, Zhao B, Bai E D. Directional differentiability of interval valued functions[J]. J. Math.Computer Sci., 2016,16:507-515.
[10] Bao Y E, Li J J, Bai E D. Study on differentiability problems of interval-valued functions[J]. J.Nonlinear Sci. Appl., 2017,10:5677-5689.
[11]代兵,包玉娥.区间数的绝对值与区间值函数的极限[J].纯粹数学与应用数学, 2016,32(6):583-590.
[12] Ying X M, Teo K L, Yang X Q. A characterization of convex function[J]. J. Math. Letters, 2000,13:27-30.
[2] Osuna-Gomez R, Chalco-Cano Y, Hernandez-Jimenez B, et al. Optimality conditions for generalized differentiable interval-valued functions[J]. Information Sciences, 2015,321:136-146.
[3] Chalco-Cano Y, Rufian-Lizan A, Roman-Flores H, et al. Calculus for interval-valued functions using generalized Hukuhara derivative and applications[J]. Fuzzy Sets and Systems, 2013,219:49-67.
[4] VanHoa N, Lupulescu V, RegandLe D. Solving interval-valued fractional initial value problems under Caputo gH-fractional differentiability[J]. Fuzzy Sets and Systems, 2017,309:1-34.
[5] Craven B D. Invex functions and constrained local minima[J]. Bull. Austral. Math. Soc., 1981,24(3):357-366.
[6] Zhang P. An interval mean-average absolute deviation model for multipored portfolio selection with risk control and cardinality constraints[J]. Soft Comput., 2016,20:1203-1212.
[7] Wu H C. On interval valued nonlinear programming problems[J]. Journal of Mathematical Analysis and Applications, 2008,338:299-316.
[8] Singh D, Dar B A, Kim D S. KKT optimality conditions in interval valued multi-objective programming with generalized differentiable functions[J]. European Journal of Operational Research,2016,254:29-39.
[9] Bao Y E, Zhao B, Bai E D. Directional differentiability of interval valued functions[J]. J. Math.Computer Sci., 2016,16:507-515.
[10] Bao Y E, Li J J, Bai E D. Study on differentiability problems of interval-valued functions[J]. J.Nonlinear Sci. Appl., 2017,10:5677-5689.
[11]代兵,包玉娥.区间数的绝对值与区间值函数的极限[J].纯粹数学与应用数学, 2016,32(6):583-590.
[12] Ying X M, Teo K L, Yang X Q. A characterization of convex function[J]. J. Math. Letters, 2000,13:27-30.