|
- 2017
实线性空间中向量优化问题近似真有效解的标量化研究
|
Abstract:
研究了实线性空间中向量优化问题的近似真有效解及其标量化.首先,指出已有结果的不合理性,通过例子对其进行了说明.其次,利用co-radiant集给出了实线性空间中一种新的近似真有效解,并对它进行了标量化研究.
In this paper, we introduce the approximate proper efficiency solutions of vector optimization problems and present their linear scalarizations. First, we point out the irrationality of the existing results and give a description by examples. Then, using the co-radiant set, we introduce a new kind of approximate proper efficiency solutions in real linear spaces and present linear scalarizations for these solutions
[1] | BENSON H P. An Improved Version of Proper Efficiency for Vector Minimization with Respect to Cones[J]. Journal of Mathematical Analysis and Applications, 1979, 71: 232-241. DOI:10.1016/0022-247X(79)90226-9 |
[2] | LALITHA C S, ARORA R. Proximal Proper Efficiency for Minimisation with Respect to Normal Cones[J]. Bull Austral Math Soc, 2005, 71: 215-224. DOI:10.1017/S0004972700038193 |
[3] | 李小燕, 高英. 多目标优化问题Proximal真有效解的最优性条件[J]. 应用数学和力学, 2015, 36(6): 668-676. DOI:10.3879/j.issn.1000-0887.2015.06.011 |
[4] | ADAN M, NOVO V. Proper Efficiency in Vector Optimization on Real Linear Spaces[J]. Journal of Optimization Theory and Applications, 2004, 121(121): 515-540. |
[5] | GUTIERREZ C, JIMENEZ B, NOVO V. A Unified Approach and Optimality Conditions for Approximate Solutions of Vector Optimization Problems[J]. SIAM Journal on Optimization, 2006, 17(3): 688-710. DOI:10.1137/05062648X |
[6] | GAO Y, YANG X M. Optimality Conditions for Approximate Solutions of Vector Optimization Problems[J]. Journal of Industrial and Management Optimization, 2011, 7(2): 483-496. DOI:10.3934/jimo |
[7] | KUHN H W, TUCKER A W. Nonlinear programming [C] //Proceeding of the Second Berkeley Symposium on Mathematical Statistics and Probability. Berkeley: University of California Press, 1951: 481-492. |
[8] | GEOFFRION A M. Proper Efficiency and the Theory of Vector Maximization[J]. Journal of Mathematical Analysis and Applications, 1968, 22: 618-630. DOI:10.1016/0022-247X(68)90201-1 |
[9] | BORWEIN J M. Proper Efficiency Points for Maximization with Respect to Cones[J]. Siam Journal on Control and Optimization, 1997, 15: 57-63. |
[10] | KUTATELADZE S S. Convex ε-Programming[J]. Soviet Mathematical Dokl, 1979, 20: 390-393. |
[11] | LORIDAN P. ε-Solutions in Vector Minimization Problems[J]. Journal of Optimization Theory and Applications, 1984, 43(2): 265-276. DOI:10.1007/BF00936165 |
[12] | GUTIERREZ C, JIMENEZ B, NOVO V. On Approximate Efficiency in Multiobjective Programming[J]. Mathematical Methods of Operations Research, 2006, 64(1): 165-185. DOI:10.1007/s00186-006-0078-0 |
[13] | 岳瑞雪, 高英. 变分不等式的解与非光滑向量优化问题拟近似解的关系[J]. 西南大学学报(自然科学版), 2016, 38(1). |
[14] | GAO Y, YANG X M. Scalarizations and Lagrange Multipliers for Approximate Solutions in the Vector Optimization Problems with Set-Valued Maps[J]. Journal of Industrial and Management Optimization, 2015, 11(2): 673-683. |
[15] | KIYANI E, SOLEIMANI-DAMANEH M. Approximate Proper Efficiency on Real Linear Vector Spaces[J]. Pacific Journal of Optimization, 2014, 10(4): 715-734. |
[16] | KOOPMANS T C. Analysis of Production as an Efficient Combination of Activities [M] //Koopmans T C. Activity Analysis of Production and Allocation. New York: John Wiley and Sons, 1951. |