OPTIMALITY CONDITIONS AND DUALITY FOR SEMI-INFINITE PROGRAMMING INVOLVING SEMILOCALLY TYPE I-PREINVEX AND RELATED FUNCTIONS
0
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
A nondifferentiable nonlinear semi-infinite programming pro\-blem is considered, where the functions involved are $\eta$-semidifferentiable type I-preinvex and related functions. Necessary and sufficient optimality conditions are obtained for a nondifferentiable nonlinear semi-infinite programming problem. Also, a Mond-Weir type dual and a general Mond-Weir type dual are formulated for the nondifferentiable semi-infinite programming problem and usual duality results are proved using the concepts of generalized semilocally type I-preinvex and related functions.
Abstract
A nondifferentiable nonlinear semi-infinite programming pro\-blem is considered, where the functions involved are $\eta$-semidifferentiable type I-preinvex and related functions. Necessary and sufficient optimality conditions are obtained for a nondifferentiable nonlinear semi-infinite programming problem. Also, a Mond-Weir type dual and a general Mond-Weir type dual are formulated for the nondifferentiable semi-infinite programming problem and usual duality results are proved using the concepts of generalized semilocally type I-preinvex and related functions.
참고문헌 (17)
- K. H. Elster, "Optimality Conditions for some Nonconvex Problems" (1980), Springer-Verlag
- G. M. Ewing, "Sufficient conditions for global minima of suitably convex functionals from variational and control theory", SIAM Rev, 19(2), pp.202~220 (1977)
- Necessary and sufficient conditions in constrained opti- mization, "M. A. Hanson", Department of Statistics, Florida State University, ~, pp.Report M683 (1984)
- M. A. Hanson, "Multiobjective programming under generalized type I invexity", J. Math. Anal. Appl, 261(2), pp.562~577 (2001)
- M. Hayashi, "Perfect duality for convexlike programs", J. Optim. Theory Appl, 38(2), pp.179~189 (1982)
- R. N. Kaul, "Generalizations of convex and related functions", European J. Oper. Res, 9(4), pp.369~377 (1982)
- S. Kaur, "Theoretical studies in mathematical programming", 박사, pp.1984
- S. K. Mishra, "Multiple objective fractional programming involving semilocally type I-preinvex and related functions", J. Math. Anal. Appl, 310(2), pp.626~640 (2005)
- S. K. Mishra, "Generalized Convexity and Vector Optimization" (2009), Springer-Verlag
- M. A. Noor, "Nonconvex functions and variational inequalities", J. Optim. Theory Appl, 87(3), pp.615~630 (1995)
- V. Preda, "Optimality and duality in fractional multiple objective programming involving semilocally preinvex and related functions", J. Math. Anal. Appl, 288(2), pp.365~382 (2003)
- V. Preda, "Duality in multiple objective programming involv- ing semilocally preinvex and related functions", Glas. Mat. Ser. III, 32(1), pp.153~165 (1997)
- V. Preda, "Optimality and duality in nonlin- ear programming involving semilocally preinvex and related functions", J. Inform. Optim. Sci, 17(3), pp.585~596 (1996)
- N. G. Rueda, "Optimality criteria in mathematical programming involving generalized invexity", J. Math. Anal. Appl, 130(2), pp.375~385 (1988)
- T. Weir, "Pre-invex functions in multiple objective optimization", J. Math. Anal. Appl, 136(1), pp.29~38 (1988)
- X. M. Yang, "On properties of preinvex functions", J. Math. Anal. Appl, 256(1), pp.229~241 (2001)
- X. M. Yang, "Semistrictly preinvex functions", J. Math. Anal. Appl, 258(1), pp.287~308 (2001)