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- Title
Nonlinear Separation Approach to Constrained Extremum Problems.
- Authors
Li, S.; Xu, Y.; Zhu, S.
- 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.
- Subjects
VARIATIONAL principles; NONLINEAR functions; METHOD of steepest descent (Numerical analysis); MATHEMATICAL optimization; EQUATIONS; NUMERICAL analysis
- Publication
Journal of Optimization Theory & Applications, 2012, Vol 154, Issue 3, p842
- ISSN
0022-3239
- Publication type
Article
- DOI
10.1007/s10957-012-0027-4