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Title: Optimality conditions for semi-infinite and generalized semi-infinite programs via lower order exact penalty functions
Authors: Yang, X 
Chen, Z
Zhou, J
Keywords: Generalized second-order derivative
Generalized semi-infinite program
Lower-order exact penalization
Optimality conditions
Semi-infinite programming
Issue Date: 2016
Publisher: Springer
Source: Journal of optimization theory and applications, 2016, v. 169, no. 3, p. 984-1012 How to cite?
Journal: Journal of optimization theory and applications 
Abstract: In this paper, we will study optimality conditions of semi-infinite programs and generalized semi-infinite programs by employing lower order exact penalty functions and the condition that the generalized second-order directional derivative of the constraint function at the candidate point along any feasible direction for the linearized constraint set is non-positive. We consider three types of penalty functions for semi-infinite program and investigate the relationship among the exactness of these penalty functions. We employ lower order integral exact penalty functions and the second-order generalized derivative of the constraint function to establish optimality conditions for semi-infinite programs. We adopt the exact penalty function technique in terms of a classical augmented Lagrangian function for the lower-level problems of generalized semi-infinite programs to transform them into standard semi-infinite programs and then apply our results for semi-infinite programs to derive the optimality condition for generalized semi-infinite programs. We will give various examples to illustrate our results and assumptions.
ISSN: 0022-3239
EISSN: 1573-2878
DOI: 10.1007/s10957-016-0914-1
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