Geodesic
Lagrange Duality and Saddle Point Optimality Conditions for Semi-Infinite Mathematical Programming Problems With Equilibrium Constraints
Yugoslav journal of operations research, Tome 29 (2019) no. 4, p. 433 .

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In this paper, we consider a special class of optimization problems which contains infinitely many inequality constraints and finitely many complementarity constraints known as the seminfinite mathematical programming problem with equilibrium constraints (SIMPEC). We propose Lagrange type dual model for the SIMPEC and obtain their duality results using convexity assumptions. Further, we discuss the saddle point optimality conditions for the SIMPEC. Some examples are given to illustrate the obtained results.
Classification : 90C33, 90C34, 90C46
Keywords: Mathematical Programming Problems With Equilibrium Constraints, Duality, Saddle Point, Semi-Infinite Programming 
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     author = {Kunwar V. K. Singh and J. K. Maurya and S. K. Mishra},
     title = {Lagrange {Duality} and {Saddle} {Point} {Optimality} {Conditions} for {Semi-Infinite} {Mathematical} {Programming} {Problems} {With} {Equilibrium} {Constraints}},
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Kunwar V. K. Singh; J. K. Maurya; S. K. Mishra. Lagrange Duality and Saddle Point Optimality Conditions for Semi-Infinite Mathematical Programming Problems With Equilibrium Constraints. Yugoslav journal of operations research, Tome 29 (2019) no. 4, p. 433 . http://geodesic.mathdoc.fr/item/YJOR_2019_29_4_a0/