Higher-order sensitivity analysis in set-valued optimization under Henig efficiency

Abstract

The behavior of the perturbation map is analyzed quantitatively by using the concept of higher-order contingent derivative for the set-valued maps under Henig efficiency. By using the higher-order contingent derivatives and applying a separation theorem for convex sets, some results concerning higher-order sensitivity analysis are established.

Optimization of fourth order Sturm-Liouville type differential inclusions with initial point constraints

“…Optimization of first order discrete and continuous time processes with lumped and distributed parameters has been expanding in all directions at an astonishing rate during the last few decades (see [1,4,5,6,7,8,11,12,13,23,24,25] and their references). The objective of the paper [1] is to briefly summarize some recent results on Differential Inclusions and their optimal control.…”

“…Then, by virtue of the generalized second-order composed contingent epiderivative, are established a unified second-order necessary and sufficient condition of optimality for set-valued optimization problems. In the paper [24] the behavior of the perturbation map is analyzed quantitatively by using the concept of higher-order contingent derivative for the set-valued maps under Henig efficiency. By using the higherorder contingent derivatives and applying a separation theorem for convex sets, some results concerning higher-order sensitivity analysis are established.…”

Optimal control of Sturm-Liouville type evolution differential inclusions with endpoint constraints

“…Optimal control of discretedifferential inclusions with lumped and distributed parameters has been expanding in all directions at an astonishing rate during the last few decades. Note that the differential inclusions are not only models for many dynamical processes but they also provide a powerful tool for various branches of mathematical analysis; see more discussions and comments in the relatively recent publications [9,20,7] and the references therein. First order differential inclusions, set-valued maps play a crucial role in the mathematical theory of optimal processes given in the next papers [2,4,6,12].…”

“…At the same time it is shown that x[•] is feasible, i.e. x(t 1 ), x (t 1 ) ∈ Q.Then by virtue of (19),(20) and second order functional transversality inclusion (c) at t = t 1 for an arbitrary feasible solution x(•) by analogy with the proof of Theorem 3.1 we deduce that J[x(t)] ≥ J[x(t)], ∀x(•), that is,x(•) is optimal.…”