This paper deals with particular families of DC optimization problems involving suprema of
convex functions. We show that the specific structure of this type of function allows us to …

On optimality conditions and duality theorems for approximate solutions of nonsmooth infinite
optimization problems | SpringerLink Skip to main content Advertisement SpringerLink Log in …

This paper aims at providing some formulae for the subdifferential and the conjungate
function of the supremum function over an arbitrary family of functions. The work is …

We provide formulae for the ε ε-subdifferential of the integral function I_f (x):= ∫ _T f (t, x) d μ
(t) I f (x):=∫ T f (t, x) d μ (t), where the integrand f: T * X → R f: T× X→ R¯ is measurable in (t …

This paper develops new extremal principles of variational analysis that are motivated by
applications to constrained problems of stochastic programming and semi-infinite …

Usually, bilevel optimization problems need to be transformed into single-level ones in order
to derive optimality conditions and solution algorithms. Among the available approaches, the …

In this paper, the robust approach (the worst case approach) for nonsmooth nonconvex
optimization problems with uncertainty data is studied. First various robust constraint …

We revisit the decoupling approach widely used (often intuitively) in nonlinear analysis and
optimization and initially formalized about a quarter of a century ago by Borwein & Zhu …

In this paper, we investigate the Moreau envelope of the supremum of a family of convex,
proper, and lower semicontinuous functions. Under mild assumptions, we prove that the …

This chapter presents a self-contained approach of variational analysis and generalized
differentiation to deriving necessary optimality conditions in bilevel optimization with …