Optimality Conditions for Generalized Ky Fan Quasi-Inequalities with Applications

Y. D. Xu () and S. J. Li ()
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Y. D. Xu: Chongqing University
S. J. Li: Chongqing University

Journal of Optimization Theory and Applications, 2013, vol. 157, issue 3, No 5, 663-684

Abstract: Abstract In this paper, the image space analysis is employed to study a generalized Ky Fan quasi-inequality with cone constraints. By virtue of a nonlinear scalarization function and a positive linear operator, a nonlinear (regular) weak separation function and a linear regular weak separation function are introduced. Nonlinear and, in particular, linear separations for the generalized Ky Fan quasi-inequality with cone constraints are characterized. Some necessary and sufficient optimality conditions, especially a saddle-point sufficient optimality condition for the generalized Ky Fan quasi-inequality with cone constraints, are obtained. As applications, some sufficient conditions for (weak) vector equilibrium flows of vector traffic equilibrium problems with capacity arc constraints, are derived.

Keywords: Image space analysis; Generalized Ky Fan quasi-inequality; Nonlinear (linear) separation function; Vector traffic equilibrium problem (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-012-0242-z

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