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Volumn 13, Issue 3, 2003, Pages 675-692

Nonlinear Lagrangian for multiobjective optimization and applications to duality and exact penalization

Author keywords

Duality; Exact penalization; Multiobjective optimization; Nonlinear Lagrangian function; Stability

Indexed keywords


EID: 0042158453     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1052623401384850     Document Type: Article
Times cited : (24)

References (23)
  • 1
    • 0000741430 scopus 로고
    • An extension of duality-stability relations to nonconvex optimization problems
    • E. J. BALDER, An extension of duality-stability relations to nonconvex optimization problems, SIAM J. Control Optim., 15 (1977), pp. 329-343.
    • (1977) SIAM J. Control Optim. , vol.15 , pp. 329-343
    • Balder, E.J.1
  • 3
    • 0026118632 scopus 로고
    • Calmness and exact penalization
    • J. V. BURKE, Calmness and exact penalization, SIAM J. Control Optim., 29 (1991), pp. 493-497.
    • (1991) SIAM J. Control Optim. , vol.29 , pp. 493-497
    • Burke, J.V.1
  • 5
    • 0035534033 scopus 로고    scopus 로고
    • A nonlinear Lagrangian theory for nonconvex optimization
    • C. J. GOH AND X. Q. YANG, A nonlinear Lagrangian theory for nonconvex optimization, J. Optim. Theory Appl., 109 (2001), pp. 99-121.
    • (2001) J. Optim. Theory Appl. , vol.109 , pp. 99-121
    • Goh, C.J.1    Yang, X.Q.2
  • 6
    • 0018441518 scopus 로고
    • Necessary and sufficient conditions for a local minimum. 3: Second-order conditions and augmented duality
    • A. D. IOFFE, Necessary and sufficient conditions for a local minimum. 3: Second-order conditions and augmented duality, SIAM J. Control Optim., 17 (1979), pp. 266-288.
    • (1979) SIAM J. Control Optim. , vol.17 , pp. 266-288
    • Ioffe, A.D.1
  • 7
    • 0027911196 scopus 로고
    • Convex composite multi-objective nonsmooth programming
    • V. JEYAKUMAR AND X. Q. YANG, Convex composite multi-objective nonsmooth programming, Math. Programming, 59 (1993), pp. 325-343.
    • (1993) Math. Programming , vol.59 , pp. 325-343
    • Jeyakumar, V.1    Yang, X.Q.2
  • 9
    • 21844506739 scopus 로고
    • Zero duality gap for a class of nonconvex optimization problems
    • D. LI, Zero duality gap for a class of nonconvex optimization problems, J. Optim. Theory Appl., 85 (1995), pp. 309-324.
    • (1995) J. Optim. Theory Appl. , vol.85 , pp. 309-324
    • Li, D.1
  • 15
    • 0021614264 scopus 로고
    • Exact penalty functions and stability in locally Lipschitz programming
    • E. ROSENBERG, Exact penalty functions and stability in locally Lipschitz programming, Math. Programming, 30 (1984), pp. 340-356.
    • (1984) Math. Programming , vol.30 , pp. 340-356
    • Rosenberg, E.1
  • 16
    • 0041760208 scopus 로고
    • Weak calmness and weak stability of multiobjective programming and exact penalty functions
    • in Chinese
    • G. Z. RUAN AND X. X. HUANG, Weak calmness and weak stability of multiobjective programming and exact penalty functions, J. Systems Sci. Math. Sci., 12 (1992), pp. 148-157 (in Chinese).
    • (1992) J. Systems Sci. Math. Sci. , vol.12 , pp. 148-157
    • Ruan, G.Z.1    Huang, X.X.2
  • 17
    • 0000606438 scopus 로고    scopus 로고
    • Modified Lagrange and penalty functions in continuous optimization
    • A. M. RUBINOV, B. M. GLOVER, AND X. Q. YANG, Modified Lagrange and penalty functions in continuous optimization, Optimization, 46 (1999), pp. 327-351.
    • (1999) Optimization , vol.46 , pp. 327-351
    • Rubinov, A.M.1    Glover, B.M.2    Yang, X.Q.3
  • 18
    • 0033261453 scopus 로고    scopus 로고
    • Decreasing functions with applications to penalization
    • A. M. RUBINOV, B. M. GLOVER, AND X. Q. YANG, Decreasing functions with applications to penalization, SIAM J. Optim., 10 (1999), pp. 289-313.
    • (1999) SIAM J. Optim. , vol.10 , pp. 289-313
    • Rubinov, A.M.1    Glover, B.M.2    Yang, X.Q.3
  • 20
    • 0021472580 scopus 로고
    • Multiobjective programming and penalty functions
    • D. J. WHITE, Multiobjective programming and penalty functions, J. Optim. Theory Appl., 43 (1984), pp. 583-599.
    • (1984) J. Optim. Theory Appl. , vol.43 , pp. 583-599
    • White, D.J.1
  • 21
    • 0000812673 scopus 로고    scopus 로고
    • Second-order global optimality conditions for convex composite optimization
    • X. Q. YANG, Second-order global optimality conditions for convex composite optimization, Math. Programming, 81 (1998), pp. 327-347.
    • (1998) Math. Programming , vol.81 , pp. 327-347
    • Yang, X.Q.1
  • 22
    • 0033439649 scopus 로고    scopus 로고
    • Optimality conditions for optimization problems with complementarity constraints
    • J. J. YE, Optimality conditions for optimization problems with complementarity constraints, SIAM J. Optim., 9 (1999), pp. 374-387.
    • (1999) SIAM J. Optim. , vol.9 , pp. 374-387
    • Ye, J.J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.