On second-order Fritz John type optimality conditions in nonsmooth multiobjective programming

被引：46
|
作者：
Gutierrez, C. [2 ]
Jimenez, B. [1 ]
Novo, V. [1 ]
机构：
[1] Univ Nacl Educ Distancia, Dept Matemat Aplicada, ETSI Ind, E-28040 Madrid, Spain
[2] Univ Valladolid, Dept Matemat Aplicada, ETSI Informat, E-47011 Valladolid, Spain
来源：
MATHEMATICAL PROGRAMMING | 2010年 / 123卷 / 01期
关键词：
Multiobjective optimization; Optimality conditions; Parabolic second order derivative; Lagrange multipliers; Second order Clarke subdifferential; DIFFERENTIABLE VECTOR OPTIMIZATION; TANGENT SETS; DIRECTIONAL-DERIVATIVES; MINIMIZATION PROBLEMS; BANACH-SPACES; CONSTRAINTS; 1ST;
D O I：
10.1007/s10107-009-0318-1
中图分类号：
TP31 [计算机软件];
学科分类号：
081202 ; 0835 ;
摘要：
We study a multiobjective optimization program with a feasible set defined by equality constraints and a generalized inequality constraint. We suppose that the functions involved are Fr,chet differentiable and their Fr,chet derivatives are continuous or stable at the point considered. We provide necessary second order optimality conditions and also sufficient conditions via a Fritz John type Lagrange multiplier rule and a set-valued second order directional derivative, in such a way that our sufficient conditions are close to the necessary conditions. Some consequences are obtained for parabolic directionally differentiable functions and C (1,1) functions, in this last case, expressed by means of the second order Clarke subdifferential. Some illustrative examples are also given.
引用
收藏
页码：199 / 223
页数：25
相关论文
共 50 条
  • [1] On second-order Fritz John type optimality conditions in nonsmooth multiobjective programming
    C. Gutiérrez
    B. Jiménez
    V. Novo
    [J]. Mathematical Programming, 2010, 123 : 199 - 223
  • [2] Second-order optimality conditions with the envelope-like effect in nonsmooth multiobjective mathematical programming II: Optimality conditions
    Phan Quoc Khanh
    Nguyen Dinh Tuan
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2013, 403 (02) : 703 - 714
  • [3] SECOND-ORDER OPTIMALITY CONDITIONS AND DUALITY FOR NONSMOOTH MULTIOBJECTIVE OPTIMIZATION PROBLEMS
    Van Luu D.
    [J]. Applied Set-Valued Analysis and Optimization, 2022, 4 (01): : 41 - 54
  • [4] On second-order Fritz John type optimality conditions for a class of differentiable optimization problems
    Feng, Min
    Li, Shengjie
    [J]. APPLICABLE ANALYSIS, 2020, 99 (15) : 2592 - 2606
  • [5] Second-order strong optimality and duality for nonsmooth multiobjective fractional programming with constraints
    Chen, Jiawei
    Liu, Luyu
    Lv, Yibing
    Ghosh, Debdas
    Yao, Jen Chih
    [J]. POSITIVITY, 2024, 28 (03)
  • [6] SECOND-ORDER OPTIMALITY CONDITIONS FOR NONSMOOTH MULTIOBJECTIVE OPTIMIZATION SUBJECTED TO MIXED CONSTRAINTS
    Tung, Nguyen Minh
    Cuong, Nguyen Minh
    [J]. Applied Set-Valued Analysis and Optimization, 2025, 7 (01): : 39 - 55
  • [7] First- and second-order optimality conditions for multiobjective fractional programming
    Khanh, P. Q.
    Tung, L. T.
    [J]. TOP, 2015, 23 (02) : 419 - 440
  • [8] First- and second-order optimality conditions for multiobjective fractional programming
    P. Q. Khanh
    L. T. Tung
    [J]. TOP, 2015, 23 : 419 - 440
  • [9] Second-order optimality conditions in nonsmooth optimization
    Ivanov, Vsevolod I.
    [J]. COMPTES RENDUS DE L ACADEMIE BULGARE DES SCIENCES, 2007, 60 (10): : 1053 - 1058
  • [10] Optimality Conditions for Nonsmooth Multiobjective Programming
    Wang, Cailing
    Zhang, You
    Sun, Wenjuan
    [J]. 2008 CHINESE CONTROL AND DECISION CONFERENCE, VOLS 1-11, 2008, : 3049 - +
12345