From Scalar to Vector Optimization

Necessary conditions for vector optimization in infinite dimension

“…functions, see e. g. [2,9,10,16,17,19,20,21,22] and references therein. We recall that a C 1,1 function is a function which is differentiable with a locally Lipschitz derivative.…”

“…The problem (1) was studied e. g. in [16,17,18,19,20,26,27,32]. The obtained results were surpassed in 2011, when I. Ginchev [14] and D. Bednařík with K. Pastor [8] published indepedently the following equivalent result (Theorem 1.1).…”

Errata: Elimination of Strict Convergence in Optimization

“…Motivated by [GGR], in [BP2] we have generalized the second-order sufficient unconstrained optimality conditions [BZ,Theorem 3.2], [GGR,Theorem 2], [BP1,Theorem 3.2], and [CC,Proposition 5.2] by the following way.…”

Derivatives of Hadamard type in scalar constrained optimization

“…Various second-order optimality conditions have been presented for optimization problems with C 1,1 functions (see e. g. [10,11,17,18,19,20,26,27,34,35,36]). We recall that a function f : R n → R is a C 1,1 function near x ∈ R n if it is (Gâteaux) differentiable on some neighbourhood of x and its derivative f (·) is Lipschitz there.…”