### Optimality conditions on nonsmooth vector interval-valued optimization

QIAN Xin-qiang, WANG Kai-rong*

1. College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China
• Published:2020-11-17

Abstract: By using Clarke directional derivative and Clarke subdifferential, Fritz John optimal necessary conditions for weak LU efficient solutions of nonsmooth vector interval-valued optimization are obtained. Under the assumption of generalized invariant convexity and regularity of functions, KKT necessary optimality conditions, sufficient optimality conditions and related duality results are given. Some examples are used to verify the feasibility of the theory. These conclusions can solve the related problems of vector interval-valued optimization in general.

CLC Number:

• O221
 [1] WU H C. The Karush-Kuhn-Tucker 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. Wolfe duality for interval-valued optimization[J]. Journal of Optimization Theory and Applications, 2008, 138(3):497-509.[3] WU H C. The Karush-Kuhn-Tucker optimality conditions in multiobjective programming problems with interval-valued objective functions[J]. European Journal of Operational Research, 2009, 196(1):49-60.[4] SUN Y H, WANG Laishen. Optimality conditions and duality in nondifferentiable interval-valued programming[J]. Journal of Industrial & Management Optimization, 2013, 9(1):131-142.[5] ANTCZAK T. Optimality conditions and duality results for nonsmooth vector optimization problems with the multiple interval-valued objective function[J]. Acta Mathematica Scientia, 2017, 37(4):1133-1150.[6] CHEN Xiuhong, LI Zhihua. On optimility conditions and duality for non-differentiable interval-valued programming problems with the generalized(F, ρ)convexity[J]. J Ind Mang Optim, 2018, 14(3):895-912.[7] JAYSWAL A, AHMAD I, BANERJEE J. Nonsmooth interval-valued optimization and saddle-point optimality criteria[J]. Bulletin of the Malaysian Mathematical Sciences Society, 2016, 39(4):1391-1411.[8] CLARKE F H. Nonsmooth optimization[M]. New York: Wiley Interscience, 1983.
 [1] WANG Hai-quan, CHONG Ge-zi. Local Gevrey regularity and analyticity of the solutions to the initial value problem associated with the two-component Novikov system [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(6): 56-63. [2] XU Xiu-juan, YAN Shuo, ZHU Ye-qing. Global regularity for very weak solutions to non-homogeneous A-harmonic equation [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(2): 48-56. [3] QI Ping, WANG Fu-cheng, WANG Bi-qing, LIANG Chang-yong. Dynamic level scheduling algorithm for cloud computing based on failure regularity-aware [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(1): 103-115. [4] . Regularity for solutions of elliptic obstacle problems with subcritical growth [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(6): 57-63. [5] LI Xiao-juan, GAO Qiang. Regularity for product space under sublinear expectation framework [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(4): 66-75. [6] LI Feng-ping, CHEN Guang-xia. Regularity criteria for weak solutions to the 3D magneto-micropolar fluid equations [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(05): 60-67. [7] GUO Jing1, CHEN Xiang-en1, WANG Zhi-wen2. Irregular assignments of the union of several vertex-disjoint #br# paths with order n [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(06): 18-25. [8] LIN Rong1,2, FAN Cheng-xian3. Function P-sets and dynamic characteristics of information regularity [J]. J4, 2012, 47(1): 121-126. [9] DAI Li-mei. Regularity of viscosity solutions to Hessian equations [J]. J4, 2010, 45(9): 62-64. [10] JIAO Tie-Ke. The eventually regularity on a class subsemirings of a semiring [J]. J4, 2009, 44(8): 56-57. [11] LIU Hong-ping,MENG Guang-wu . F*-Paracompactness in L-topological spaces [J]. J4, 2008, 43(3): 75-79 .
Viewed
Full text

Abstract

Cited

Shared
Discussed