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Unified nonlinear Lagrangian approach to duality and optimal paths. (English) Zbl 1145.90450

Summary: In the context of an inequality constrained optimization problem, we present a unified nonlinear Lagrangian dual scheme and establish necessary and sufficient conditions for the zero duality gap property. From these results, we derive necessary and sufficient conditions for four classes of zero duality gap properties and establish the equivalence among them. Finally, we obtain the convergence of an optimal path for the unified scheme and present a sufficient condition for the finite termination of the optimal path.

MSC:

90C31 Sensitivity, stability, parametric optimization
90C46 Optimality conditions and duality in mathematical programming
49N15 Duality theory (optimization)
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