On saddle points in nonconvex semi-infinite programming
In this paper we apply two convexification procedures to the Lagrangian of a nonconvex semi-infinite programming problem. Under the reduction approach it is shown that, locally around a local minimizer, this problem can be transformed equivalently in such a way that the transformed Lagrangian fulfills saddle point optimality conditions, where for the first procedure both the original objective function and constraints (and for the second procedure only the constraints) are substituted by their pth powers with sufficiently large power p. These results allow that local duality theory and corresponding numerical methods (e.g. dual search) can be applied to a broader class of nonconvex problems. Copyright Springer Science+Business Media, LLC. 2012
Volume (Year): 54 (2012)
Issue (Month): 3 (November)
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- Qingxiang Zhang, 2009. "Optimality conditions and duality for semi-infinite programming involving B-arcwise connected functions," Computational Optimization and Applications, Springer, vol. 45(4), pages 615-629, December.
- Nader Kanzi, 2011. "Necessary optimality conditions for nonsmooth semi-infinite programming problems," Journal of Global Optimization- An International Journal Dealing with Theoretical and Computational Aspects of Seeking Global Optima and Their Applications in Science, Management and Engineering, Springer, vol. 49(4), pages 713-725, April.
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