Nonlinear Analysis: Theory, Methods & Applications
Sequential Convex Subdifferential Calculus and Sequential Lagrange Multipliers
SIAM Journal on Control and Optimization
Exact Penalization and Necessary Optimality Conditions for Generalized Bilevel Programming Problems
SIAM Journal on Optimization
Characterizing Set Containments Involving Infinite Convex Constraints and Reverse-Convex Constraints
SIAM Journal on Optimization
Convex Optimization
Liberating the Subgradient Optimality Conditions from Constraint Qualifications
Journal of Global Optimization
Some new Farkas-type results for inequality systems with DC functions
Journal of Global Optimization
On Nash---Cournot oligopolistic market equilibrium models with concave cost functions
Journal of Global Optimization
SIAM Journal on Optimization
Duality and optimality conditions for generalized equilibrium problems involving DC functions
Journal of Global Optimization
SIAM Journal on Optimization
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In this paper we extend some results in [Dinh, Goberna, López, and Volle, Set-Valued Var. Anal., to appear] to the setting of functional inequalities when the standard assumptions of convexity and lower semicontinuity of the involved mappings are absent. This extension is achieved under certain condition relative to the second conjugate of the involved functions. The main result of this paper, Theorem 1, is applied to derive some subdifferential calculus rules and different generalizations of the Farkas lemma for nonconvex systems, as well as some optimality conditions and duality theory for infinite nonconvex optimization problems. Several examples are given to illustrate the significance of the main results and also to point out the potential of their applications to get various extensions of Farkas-type results and to the study of other classes of problems such as variational inequalities and equilibrium models.