Paper Info
Title
Optimality Conditions for Semi-Infinite and Generalized Semi-Infinite Programs Via Lower Order Exact Penalty Functions.
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.
Year
DOI
Venue
2016
10.1007/s10957-016-0914-1
J. Optimization Theory and Applications
Keywords
Field
DocType
Semi-infinite programming, Generalized semi-infinite program, Optimality conditions, Lower-order exact penalization, Generalized second-order derivative, 49M30, 90C34, 90C46
Mathematical optimization,Mathematical analysis,Semi-infinite,Semi-infinite programming,Augmented Lagrangian method,Directional derivative,Mathematics,Penalty method
Journal
Volume
Issue
ISSN
169
3
1573-2878
Citations 
PageRank 
References 
1
0.36
15
Authors
3
Name
Order
Citations
PageRank
Xiaoqi Yang112620.85
Zhe Chen231.33
Jinchuan Zhou3298.23