Nonlinear Separation Approach to Constrained Extremum Problems |
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Authors: | S. J. Li Y. D. Xu S. K. Zhu |
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Affiliation: | 1. College of Mathematics and Statistics, Chongqing University, Chongqing, 401331, China 2. Mathematical Sciences Research Institute in Chongqing, Chongqing University, Chongqing, 401331, China
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Abstract: | In this paper, by virtue of a nonlinear scalarization function, two nonlinear weak separation functions, a nonlinear regular weak separation function, and a nonlinear strong separation function are first introduced, respectively. Then, by the image space analysis, a global saddle-point condition for a nonlinear function is investigated. It is shown that the existence of a saddle point is equivalent to a nonlinear separation of two suitable subsets of the image space. Finally, some necessary and sufficient optimality conditions are obtained for constrained extremum problems. |
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