Abstract
In this paper, we establish relations between a solution of a vector continuous-time program and a solution of a vector variational-type inequality problem with functionals.
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C. Baiocchi and A. Capelo,Variational and Quasi-Variational Inequalities Applications to Free-boundary Problems, John Wiley, 1994.
C. R. Bector and I. Husain,Duality for multiobjective variational problems, J. Math. Anal. Appl.166 (1992), 214–229.
D. Bhatia and P. Kumar,Multiobjective control problem with generalized invexity, J. Math. Anal. Appl.189 (1995), 676–692.
A. M. Geoffrion,Proper efficiency and the theory of vector maximization, J. Math. Anal. Appl.22 (1968), 618–630.
F. Giannessi,Theorems of alternative, quadratic programs and complementarity problem in “Variational Inequalities and Complementarity Problems”, edited by R. W. Cottle, F. Giannessi and J. L. Lions, Wiley, Chichester, England, pp. 151–186, 1980.
F. Giannessi, “On Minty variational principle” inNew Trends in Mathematical Programming, Kluwer Academic Publishers, 93–99, 1998.
G. M. Lee, “On relations between vector variational inequality and vector optimization problem” in: X. Q. Yang et al. eds.,Progress in Optimization, Kluwer Academic Publishers, pp. 167–179, 2000.
G. M. Lee, D. S. Kim, B. S. Lee and N. D. Yen,Vector variational inequality as a tool for studying vector optimization problems, Nonlinear Anal. Theory Meth. Appl.34 (1998), 745–765.
G. M. Lee and M. H. Kim,Remarks on relations between rector variational inequality and vector optimization problem, Nonlinear Anal. Theory Meth. Appl.47 (2001), 627–635.
G. M. Lee and M. H. Kim,On second order necessary optimality conditions for vector optimization problems, J. Korean Math. Soc.40 (2003), 287–305.
S. K. Mishra and R. N. Mukherjee,On efficiency and duality for multiobjective variational problems, J. Math. Anal. Appl.187 (1994), 40–54.
S. K. Mishra and R. N. Mukherjee,Multiobjective control problem with V-invexity, J. Math. Anal. Appl.235 (1999), 1–12.
X. Q. Yang, Generalized convex functions and vector variational inequalities, J. Optim. Theory Appl.79 (1993), 563–580.
X. Q. Yang,Vector variational inequality and vector pseudolinear optimization, J. Optim. Theory Appl.95 (1997), 729–734.
X. Q. Yang, “On some equivalent conditions of vector variational inequalities”, in: F. Giannessi ed.,Vector Variational Inequalities and Vector Equilibria, Kluwer Academic Publishers, pp. 423–432, 2000.
G. J. Zalmai,Optimality conditions and duality for a class of continuous-time programming problems with nonlinear operator equality and inequality constraints, J. Math. Anal. Appl.153 (1990), 309–330.
G. J. Zalmai,Generalized sufficient criteria in continuous-time programming with application to a class of variational-type inequalities, J. Math. Anal. Appl.153 (1990), 331–355.
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This work was supported by Korea Research Foundation Grant. (KRF-2002-037-C00006)
Moon Hee Kim received her Ph. D at Pukyong National University under the direction of Professor Gue Myung Lee. Since 2000, she has been at the Pukyong National University as a lecturer. Her research interests focus on vector optimization problem and variational inequality.
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Kim, M.H. Relations between vector continuous-time program and vector variational-type inequality. JAMC 16, 279–287 (2004). https://doi.org/10.1007/BF02936168
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DOI: https://doi.org/10.1007/BF02936168