Optimality Conditions for Semi-Infinite and Generalized Semi-Infinite Programs Via Lower Order Exact Penalty Functions

Xiaoqi Yang (), Zhangyou Chen () and Jinchuan Zhou ()
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Xiaoqi Yang: The Hong Kong Polytechnic University
Zhangyou Chen: South-West Jiao Tong University
Jinchuan Zhou: Shandong University of Technology

Journal of Optimization Theory and Applications, 2016, vol. 169, issue 3, No 14, 984-1012

Abstract: 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: Semi-infinite programming; Generalized semi-infinite program; Optimality conditions; Lower-order exact penalization; Generalized second-order derivative; 49M30; 90C34; 90C46 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10957-016-0914-1

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