Article citationsMore>>

Izmailov, A.F. and Solodov, M.V. (2009) Mathematical Programs with Vanishing Con-straints: Optimality Conditions, Sensitivity, and a Relaxation Method. Journal of Optimization Theory and Applications, 142, 501-532.
https://doi.org/10.1007/s10957-009-9517-4

has been cited by the following article:

• TITLE: Some Convexificators-Based Optimality Conditions for Nonsmooth Mathematical Program with Vanishing Constraints

  AUTHORS: Qingjie Hu, Zhijuan Zhou, Yu Chen

  KEYWORDS: Mathematical Program with Vanishing Constraints, Optimality Conditions, Convexificator

  JOURNAL NAME: American Journal of Operations Research, Vol.11 No.6, November 22, 2021

  ABSTRACT: In this paper, by using the notion of convexificator, we introduce the generalized standard Abadie constraint qualification and the generalized MPVC Abadie constraint qualification, and define the generalized stationary conditions for the nonsmooth mathematical program with vanishing constraints (MPVC for short). We show that the generalized strong stationary is the first order necessary optimality condition for nonsmooth MPVC under the generalized standard Abadie constraint qualification. Sufficient conditions for global or local optimality for nonsmooth MPVC are also derived under some generalized convexity assumptions.