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In Section 3, we introduce the generalized Guignard constraint qualification and Abadie constraint qualification for SIMOPs.
Now, we give a generalized Slater type constraint qualification.
Furthermore, let (VP) satisfies the generalized Slater constraint qualification.
In theory its constraints fail to satisfy a standard constraint qualification such as the linear independence constraint qualification (LICQ) or the Mangasarian–Fromovitz constraint qualification (MFCQ) at any feasible point.
We propose a generalized Guignard constraint qualification and a generalized Abadie constraint qualification for this problem under which necessary optimality conditions are proved.
Necessary optimal theorems are presented by using alternative theorem [15] and Mangasarian-Fromovitz constraint qualification [16].
To derive necessary optimality conditions one needs to impose some kind of constraint qualification.
FM is well known as a necessary and sufficient constraint qualification for Lagrange duality; see [1].
By the generalized Slater constraint qualification, then there exists such that (5.18).
The Fritz-John conditions and the constraint qualification are discussed for this problem.
The constraint qualification and optimality condition for the SOCBLP are studied in Section 4.
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