Optimization: algorithms and consistent approximations
Optimization: algorithms and consistent approximations
Generalized semi-infinite optimization: a first order optimality condition and examples
Mathematical Programming: Series A and B
Mathematics of Operations Research
Mathematical Programs with Complementarity Constraints: Stationarity, Optimality, and Sensitivity
Mathematics of Operations Research
Mathematics of Operations Research
A Branch-and-Bound Approach for Solving a Class of Generalized Semi-infinite Programming Problems
Journal of Global Optimization
Operations Research
BI-Level Strategies in Semi-Infinite Programming
BI-Level Strategies in Semi-Infinite Programming
Interval methods for semi-infinite programs
Computational Optimization and Applications
Global solution of semi-infinite programs
Mathematical Programming: Series A and B
On the Use of Augmented Lagrangians in the Solution of Generalized Semi-Infinite Min-Max Problems
Computational Optimization and Applications
The Adaptive Convexification Algorithm: A Feasible Point Method for Semi-Infinite Programming
SIAM Journal on Optimization
Relaxation-Based Bounds for Semi-Infinite Programs
SIAM Journal on Optimization
Global solution of bilevel programs with a nonconvex inner program
Journal of Global Optimization
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This paper introduces novel numerical solution strategies for generalized semi-infinite optimization problems (GSIP), a class of mathematical optimization problems which occur naturally in the context of design centering problems, robust optimization problems, and many fields of engineering science. GSIPs can be regarded as bilevel optimization problems, where a parametric lower-level maximization problem has to be solved in order to check feasibility of the upper level minimization problem. The current paper discusses several strategies to reformulate this class of problems into equivalent finite minimization problems by exploiting the concept of Wolfe duality for convex lower level problems. Here, the main contribution is the discussion of the non-degeneracy of the corresponding formulations under various assumptions. Finally, these non-degenerate reformulations of the original GSIP allow us to apply standard nonlinear optimization algorithms.