Generalized semi-infinite optimization: a first order optimality condition and examples
Mathematical Programming: Series A and B
First-order optimality conditions in generalized semi-infinite programming
Journal of Optimization Theory and Applications
Optimality Conditions for a Class of Mathematical Programs with Equilibrium Constraints
Mathematics of Operations Research
SIAM Journal on Control and Optimization
Weakly upper Lipschitz multifunctions and applications in parametric optimization
Mathematical Programming: Series A and B
Metric regularity of semi-infinite constraint systems
Mathematical Programming: Series A and B
Mathematics of Operations Research
Lagrange Multipliers in Nonsmooth Semi-Infinite Optimization Problems
Mathematics of Operations Research
SIAM Journal on Optimization
Metric Regularity in Convex Semi-Infinite Optimization under Canonical Perturbations
SIAM Journal on Optimization
Subgradients of marginal functions in parametric mathematical programming
Mathematical Programming: Series A and B - Nonlinear convex optimization and variational inequalities
SIAM Journal on Optimization
Mathematical Programming: Series A and B - Series B - Special Issue: Well-posedness, stability and related topics
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This paper proposes two new constraint qualification conditions (CQs) which are useful for a unified study of CQs from both a convex analysis and a nonsmooth analysis point of view. Our CQs cover the existing CQs of Mangasarian-Fromovitz and Farkas-Minkowski types. Some sufficient conditions for the validity of the new CQs are given. Under these CQs, we derive formulae for computing and/or estimating the (basic and singular) subdifferentials of marginal/optimal value function in semi-infinite programming from some results of modern variational analysis and generalized differentiation. Examples are given to illustrate the obtained formulae.