Approximate optimality conditions and approximate duality theorems for nonlinear semi-infinite programming problems with uncertainty data. (English) Zbl 1515.90107
Summary: In this paper, we establish optimality conditions and duality theorems for a robust \(\varepsilon\)-quasi solution of a nonsmooth semi-infinite programming problem with data uncertainty in both the objective and constraints. Next, we provide an application to nonsmooth fractional semi-infinite optimization problem with data uncertainty in constraints. Finally, some examples are given to illustrate the obtained results.
MSC:
| 90C26 | Nonconvex programming, global optimization |
| 49J52 | Nonsmooth analysis |
| 65K10 | Numerical optimization and variational techniques |
| 90C34 | Semi-infinite programming |
| 90C46 | Optimality conditions and duality in mathematical programming |
| 90C47 | Minimax problems in mathematical programming |
Keywords:
semi-infinite programming; approximate optimality condition; approximate duality; Clarke subdifferential; robust optimizationReferences:
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