Generalized second-order directional derivatives and optimality conditions

Second-Order Optimality Conditions in Generalized Semi-Infinite Programming

This paper deals with generalized semi-infinite optimization problems where the (infinite) index set of inequality constraints depends on the state variables and all involved functions are twice continuously differentiable. Necessary and sufficient second order optimality conditions for such problems are derived under assumptions which imply that the corresponding optimal value function is seco...

Generalized second-order parametric optimality conditions in semiinfinite discrete minmax fractional programming and second order (F

This paper deals with mainly establishing numerous sets of generalized second-order parametric sufficient optimality conditions for a semiinfinite discrete minmax fractional programming problem, while the results on semiinfinite discrete minmax fractional programming problem are achieved based on some partitioning schemes under various types of generalized second-order (F ,β, φ, ρ, θ, m)-univex...

On Directional Metric Subregularity and Second-Order Optimality Conditions for a Class of Nonsmooth Mathematical Programs

We study infinite dimensional optimization problems where the constraint mapping is given as the sum of a smooth function and a generalized polyhedral multifunction, e.g. the normal cone mapping of a convex polyhedral set. By using advanced techniques of variational analysis we obtain first-order and second-order characterizations, both necessary and sufficient, for directional metric subregula...

Second-order optimality conditions for nonlinear programs and mathematical programs

It is well known that second-order information is a basic tool notably in optimality conditions and numerical algorithms. In this work, we present a generalization of optimality conditions to strongly convex functions of order γ with the help of first- and second-order approximations derived from (Optimization 40(3):229-246, 2011) and we study their characterization. Further, we give an example...

Marginal values and second-order necessary conditions for optimality