Abstract
The image space approach is applied to the study of vector variational inequalities. Exploiting separation arguments in the image space, Lagrangian type optimality conditions and gap functions for vector variational inequalities are derived.
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References
Auslender A. (1976) Optimization. Methodes Numeriques, Masson, Paris;
Berman A. (1973) Cones, matrices and mathematical programming, Lecture Notes in Economics and Mathematical Systems, Springer-Verlag, Berlin, Germany;
Castellani M., Mastroeni G., and Pappalardo M. (1996) On regularity for generalized systems and applications, in “Nonlinear Optimization and Applications”, G. Di Pillo, F.Giannessi (eds.), Plenum Press, New York, pp. 13–26;
Dien P.H., Mastroeni G., Pappalardo M., and Quang P.H. (1994) Regularity Conditions for Constrained Extremum Problems via Image Space: the Linear Case, in Generalized Convexity, Lecture Notes in Economics and Mathematical Systems, S. Komlosi, T. Rapcsak and S. Schaible (eds.), Springer Verlag, Berlin, Germany, pp. 145–152;
Fukushima M. (1992) Equivalent differentiable optimization problems and descent methods for asymmetric variational inequality problems,Mathematical Programming, Vol. 53, pp. 99–110;
Giannessi F. (1998) On Minty Variational Principle, in “New Trends in Mathematical Programming”, F.Giannessi, S.Komlosi, T.Rapcsak (eds. ), Kluwer;
Giannessi F. (1980) Theorems of the Alternative, Quadratic Programs and Cornplementarity Problems, in “Variational Inequalities and Complementarity Problems”,R.W. Cottle, F. Giannessi and J.L. Lions (eds.), Wiley, New York, pp.151186;
Giannessi F. (1995) Separation of sets and Gap Functions for Quasi-Variational Inequalities, in “Variational Inequalities and Network Equilibrium Problems”, F.Giannessi and A.Maugeri (eds.),Plenum Publishing Co, pp.101–121;
Giannessi F. (1984) Theorems of the Alternative and Optimality Conditions, Journal of Optimization Theory and Applications, Vol. 42, pp. 331–365;
Harker P.T.,Pang J.S. (1990) Finite—Dimensional Variational Inequalities and Nonlinear Complementarity Problem: a Survey of Theory, Algorithms and Applications, Mathematical Programming, Vol. 48, pp. 161–220;
Lee G.M., Kim D.S., Lee B.S. and Yen N.D. (1998) Vector Variational Inequality as a tool for studying Vector Optimization Problems, Nonlinear Analysis, Vol. 34, pp. 745–765;
Maeda T. (1994) Constraint Qualifications in Multiobjective Optimization Problems: Differentiable Case, Journal of Optimization Theory and Applications, Vol. 80, pp. 483–500;
Mangasarian O.L. (1969) Nonlinear Programming, New York, Academic Press;
Mangasarian O.L. and Fromovitz S. (1967) The Fritz—John Necessary Optimality Condition in the Presence of Equality and Inequality Constraints, Journal of Mathematical Analysis and Applications, Vol. 7, pp. 37–47;
Rockafellar R.T. (1970) Convex Analysis, Princeton University Press, Princeton;
Zhu D.L.,Marcotte P. (1994) An extended descent framework for variational inequalities, Journal of Optimization Theory and Applications, Vol.80, pp. 349–366.
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Mastroeni, G. (2000). Separation methods for Vector Variational Inequalities. Saddle point and gap function. In: Pillo, G.D., Giannessi, F. (eds) Nonlinear Optimization and Related Topics. Applied Optimization, vol 36. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3226-9_11
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DOI: https://doi.org/10.1007/978-1-4757-3226-9_11
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