본문 바로가기
KERD
논문KCI 등재

SENSITIVITY ANALYSIS FOR A CLASS OF IMPLICIT MULTIFUNCTIONS WITH APPLICATIONS

Shengjie Li|Minghua Li
대한수학회 (The Korean Mathematical Society)|2012.03|대한수학회보 (Bulletin of the KMS)|제49권 제2호|pp. 249-262

1

조회

0

다운로드

0

인용

0

참고문헌

키워드

sensitivity analysisselectionimplicit multifunctionparametric vector optimization problem
주제분류수학

초록

In this paper, under some suitable conditions and in virtue of a selection which depends on a vector-valued function and a feasible set map, the sensitivity analysis of a class of implicit multifunctions is investigated. Moreover, by using the results established, the solution sets of parametric vector optimization problems are studied.

Abstract

In this paper, under some suitable conditions and in virtue of a selection which depends on a vector-valued function and a feasible set map, the sensitivity analysis of a class of implicit multifunctions is investigated. Moreover, by using the results established, the solution sets of parametric vector optimization problems are studied.

참고문헌 (31)

  1. T. Amaroq, "On proto-differentiability and strict proto-differentiability of multifunctions of feasible points in perturbed optimization problems", Numer. Funct. Anal. Optim, 16, pp.1293~1307 (1995)
  2. J. P. Aubin, "Applied Nonlinear Analysis" (1984), John Wiley and Sons
  3. J. P. Aubin, "Set-Valued Analysis" (1990), Birkhauser
  4. J. F. Bonnans, "Perturbation Analysis of Optimization Problems" (2000), Springer-Verlag
  5. J. M. Borwein, "Stability and regular points of inequality systems", J. Optim. Theory Appl, 48(1), pp.9~52 (1986)
  6. A. L. Dontchev, "Implicit function theorems for generalized equations", Math. Programming, 70(1), pp.91~106 (1995)
  7. A. V. Fiacco, "Introduction to Sensitivity and Stability Analysis in Nonlinear Program- ming" (1983), Academic Press
  8. A. J. King, "Sensitivity analysis for nonsmooth generalized equa- tions", Math. Programming, 55(2), pp.193~212 (1992)
  9. H. Kuk, "Sensitivity analysis in vector optimization", J. Optim. Theory Appl, 89(3), pp.713~730 (1996)
  10. A. B. Levy, "Implicit multifunction theorems for the sensitivity analysis of variational conditions", Math. Programming, 74(3), pp.333~350 (1996)
  11. A. B. Levy, "Variational conditions and the proto-differentiation of partial subgradient mappings", Nonlinear Anal, 26(12), pp.1951~1964 (1996)
  12. M. H. Li, "Second-order differential and sensitivity properties of weak vector variational inequalities", J. Optim. Theory Appl, 144(1), pp.76~87 (2010)
  13. S. J. Li, "Contingent derivatives of set-valued maps with applications to vector optimization", ~
  14. S. J. Li, "Calculus rules for derivatives of multimaps", Set-Valued Var. Anal, 17(1), pp.21~39 (2009)
  15. S. J. Li, "Differential and sensitivity properties of gap functions for vector variational inequalities", Math. Methods Oper. Res, 57(3), pp.377~391 (2003)
  16. K. W. Meng, "Differential and sensitivity properties of gap functions for Minty vector variational inequalities", J. Math. Anal. Appl, 337(1), pp.386~398 (2008)
  17. J.-P. Penot, "Differentiability of relations and differential stability of perturbed optimiza- tion problems", SIAM J. Control Optim, 22(4), pp.529~551 (1984)
  18. Y. P. Qiu, "Sensitivity analysis for variational inequalities defined on polyhedral sets", Math. Oper. Res, 14(3), pp.410~432 (1989)
  19. Y. P. Qiu, "Sensitivity analysis for variational inequalities", Math. Oper. Res, 17(1), pp.61~76 (1992)
  20. S. M. Robinson, "Generalized equations and their solutions. I. Basic theory", Math. Programming Stud, 10, pp.128~141 (1979)
  21. S. M. Robinson, "Strongly regular generalized equations", Math. Oper. Res, 5(1), pp.43~62 (1980)
  22. S. M. Robinson, "An implicit-function theorem for a class of nonsmooth functions", Math. Oper. Res, 16(2), pp.292~309 (1991)
  23. R. T. Rockafellar, "Proto-differentiability of set-valued mappings and its applications in optimization", Ann. Inst. H. Poincare Anal. Non Lineaire, 6(suppl), pp.449~482 (1989)
  24. R. T. Rockafellar, "Lagrange multipliers and subderivatives of optimal value functions in nonlinear programming", Math. Programming Stud, 17, pp.28~66 (1982)
  25. R. T. Rockafellar, "Variational Analysis" (1998), Springer
  26. Y. Sawaragi, "Theory of Multiobjective Optimization" (1985), Academic Press
  27. A. Shapiro, "On concepts of directional differentiability", J. Optim. Theory Appl, 66(3), pp.477~487 (1990)
  28. A. Shapiro, "Sensitivity analysis of parameterized variational inequalities", Math. Oper. Res, 30(1), pp.109~126 (2005)
  29. D. S. Shi, "Contingent derivative of the perturbation map in multiobjective optimization", J. Optim. Theory Appl, 70(2), pp.385~396 (1991)
  30. T. Tanino, "Sensitivity analysis in multiobjective optimization", J. Optim. Theory Appl, 56(3), pp.479~499 (1988)
  31. R. L. Tobin, "Sensitivity analysis for variational inequalities", J. Optim. Theory Appl, 48(1), pp.191~204 (1986)

관련 논문AI추천

Sensitivity Analysis for Completely Generalized Nonlinear Variational InclusionsFirdosh Khan, Salahuddin영남수학회 · East Asian Mathematical Journal2009 · 제25권 제1호Proper efficiency for set-valued optimization problems and vector variational-like inequalitiesDao-Jun Wen, Jing Quan, Xian Jun Long대한수학회 · 대한수학회보2013 · 제50권 제3호Solutions of vector variational inequality problemsSalahuddin강원경기수학회 · 한국수학논문집2018 · 제26권 제2호ON THE LOWER SEMICONTINUITY OF THE SOLUTION SETS FOR PARAMETRIC GENERALIZED VECTOR MIXED QUASIVARIATIONAL INEQUALITY PROBLEMSNguyen Van Hung대한수학회 · 대한수학회보2015 · 제52권 제6호Sensitivity Analysis for GeneralizedNonlinear Implicit Quasi-variational InclusionsJae Ug Jeong경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2006 · 제46권 제3호Sensitivity analysis of solutions for parametric nonlinear implicit quasivariational inclusionsS. E. Abbas, Weili Wang, Zeqing Liu대한수학회 · 대한수학회논문집2005 · 제20권 제2호

이 간행물의 다른 논문 (20건)

GEOMETRIC QUANTIZATION OF ODD DIMENSIONAL SPINc MANIFOLDSJian Wang, Yong Wangpp. 223-234FUNCTION ALGEBRAS ON BIDISKSKieu Phuong Chi, Nguyen Quang Dieupp. 235-247SHADOWABLE CHAIN TRANSITIVE SETS OF C1-GENERIC DIFFEOMORPHISMSXiao Wen, 이건희pp. 263-270LINEAR WEINGARTEN SPACELIKE HYPERSURFACES IN LOCALLY SYMMETRIC LORENTZ SPACEDan Yangpp. 271-284Hypersurfaces with constant $\boldsymbol{k}$-th mean curvature and two distinct principal curvatures in spheresJiancheng Liu, Yan Weipp. 285-293
원문 보기