On Mixed Type Robust Duality for Nonconvex and Nonsmooth Semi-Infinite Optimization
Nonconvex and nonsmooth semi-infinite optimization with uncertainty is an important subclass of uncertain optimization fields due to its widely applications in machine learning,signal processing and other fields.This paper is devoted to consider a class of nonconvex and nonsmooth semi-infinite optimization problems with uncertain data appearing in both the objective functions and constraints.A mixed type robust dual problem for this uncertain optimization problem in terms of robust optimization methodology.The robust weak,strong and converse duality relations between them are obtained in terms of assumptions of generalized convexity and a new robust-type subdifferential constraint qualification.
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