Nonlinear separation functions,optimality conditions and error bounds for Ky Fan quasi-inequalities |
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Authors: | Y D Xu |
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Institution: | 1.College of Science,Chongqing University of Posts and Telecommunications,Chongqing,China |
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Abstract: | In this paper, we employ the image space analysis to investigate a Ky Fan quasi-inequality with cone constraints. By means of the oriented distance function, a new nonlinear weak (regular) separation function is introduced. Some necessary and sufficient optimality conditions, especially, a saddle-point sufficient optimality condition for the Ky Fan quasi-inequality with cone constraints, are obtained. By virtue of the nonlinear regular weak separation function, a gap function for the Ky Fan quasi-inequality with cone constraints is obtained. Moreover, we get an error bound for the solution set of the Ky Fan quasi-inequality with respect to the gap function under strongly monotone assumptions. |
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