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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
Issue Date: Mar-2016
Source: Journal of optimization theory and applications, Mar. 2016, v. 169, no. 3, p. 984-1012
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.
Keywords: Generalized second-order derivative
Generalized semi-infinite program
Lower-order exact penalization
Optimality conditions
Semi-infinite programming
Publisher: Springer
Journal: Journal of optimization theory and applications 
ISSN: 0022-3239
EISSN: 1573-2878
DOI: 10.1007/s10957-016-0914-1
Rights: © Springer Science+Business Media New York 2016
This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use (, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at:
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