Normal subdifferentials of efficient point multifunctions in parametric vector optimization (Q360483)

The following notations are introduced: \(P\), \(X\), \(Y\) are Banach spaces, elements of \(P\) are interpreted as parameters, \(f: P\times X\mapsto X\) is a vector function, \(C: P\to X\) is a multifunction, \(K\), \(K\subseteq Y\) is a convex cone such that \(K\cap(-K)= \{0\}\). The cone \(K\) induces a partial order \(\leq_K\), i.e. for any \(y^{(1)}, y^{(2)}\in Y\), \(y^{(1)}\leq_K y^{(2)}\) if and only if \((y^{(1)}- y^{(2)})\in K\). Let symbol \(\text{Min}_KA\) denote the set of efficient points of \(A\), \(A\subseteq Y\), with respect to \(K\), i.e. \(\text{Min}_KA\) is the set of points \(y\), for which \((y- K)\cap A= \{y\}\). The author introduces multifunctions \[ F(p)\equiv \{f(p,x): x\in C(p)\},\;R(p)\equiv \text{Min}_K F(p),\;p\in P \] and studies properties of \(R(p)\). New formulae for computing and estimating the normal subdifferential of \(R(p)\) are established. The paper was motivated by sensitivity analysis in parametric vector optimization problems.