Sensitivity analysis in convex programming

Sensitivity Analysis in Convex Optimization through the Circatangent Derivative

“…for every b ∈ V. The proof 2 of Lemma 2 in [10] yields that T Υ is continuously Fréchet differentiable at b 0 , and thus, by Theorem 5 and Theorem 10 in [5] we obtain that…”

“…for every u ∈ Z. Consequently,φ is continuously Fréchet differentiable at b 0 and To finish the proof, let us note that (19) immediately follows from Theorem 6 in [10], since every tangentially regular set-valued map is derivable and its circatangent and contingent derivatives coincide.…”

“…Following this methodology, the sensitivity of a differential vector optimization problem with equality constraints was analysed in [9]. Similarly, the sensitivity of a convex vector problem with inequality constraints was studied in [10]. In both cases, the study was carried out by analysing the derivability and by computing the contingent derivative of the set-valued map solution.…”

“…In both cases, the study was carried out by analysing the derivability and by computing the contingent derivative of the set-valued map solution. In this paper, we deal with the same problem as in [10], but focusing on the tangential regularity of the set-valued solution map and the computation of its circatangent derivative, also called Clarke derivative.…”

A natural extension of the classical envelope theorem in vector differential programming

“…In this work, by applying a selection in the efficient set, two versions of the envelope theorem for differentiable and convex programs were stated. In the paper the authors used the so-called T -optimal solutions, concept successfully utilized in many other works of sensitivity analysis [13][14][15][16][17][18][19][20][21][22]. These solutions are characterized to become minimum when the objective function is composed with a positive function, T , and under weak requirements are dense in the efficient set.…”