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

Xiaoqi Yang, Zhangyou Chen, Jinchuan Zhou

Research output: Journal article publicationJournal articleAcademic researchpeer-review

5 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)984-1012
Number of pages29
JournalJournal of Optimization Theory and Applications
Issue number3
Publication statusPublished - 1 Jun 2016


  • Generalized second-order derivative
  • Generalized semi-infinite program
  • Lower-order exact penalization
  • Optimality conditions
  • Semi-infinite programming

ASJC Scopus subject areas

  • Control and Optimization
  • Management Science and Operations Research
  • Applied Mathematics

Cite this