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http://hdl.handle.net/10397/61531
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. | URI: | http://hdl.handle.net/10397/61531 | ISSN: | 0022-3239 | EISSN: | 1573-2878 | DOI: | 10.1007/s10957-016-0914-1 |
Appears in Collections: | Journal/Magazine Article |
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