Search Results - derivatives AND coderivatives

Coderivative and Graphical Derivative of the Metric Projection onto Closed Balls in Hilbert Spaces by Hien, Le Van

“…In this paper, we first derive an exact formula for computing the regular coderivative of the metric projection operator onto closed balls r B centered at the origin in Hilbert spaces…”
Get full text

Optimality Conditions for Approximate Pareto Minimality by Durea, Marius

“…In this paper, we apply, to the case of approximate minimizers for vector optimization problems with set-valued maps, some techniques developed previously in…”
Get full text

Generalized Newton’s method based on graphical derivatives by Hoheisel, T., Kanzow, C., Mordukhovich, B.S., Phan, H.

“… We propose and justify a new generalized Newton algorithm based on graphical derivatives, which have never been used to derive a Newton-type method for solving nonsmooth equations…”
Get full text

A Derivative-Coderivative Inclusion in Second-Order Nonsmooth Analysis by Rockafellar, R. T., Zagrodny, D.

Get full text

Regular Coderivative and Graphical Derivative of the Metric Projection onto closed Balls in Hilbert spaces by Le Van Hien

“…In this paper, we first establish a formula for exactly computing the regular coderivative of the metric projection operator onto closed balls \(r\mathbb{B…”
Get full text

On Second-Order Variational Analysis of Variational Convexity of Prox-Regular Functions by Gfrerer, Helmut

“… In this paper we present second-order characterizations of these properties, i.e., conditions using first-order generalized derivatives of the subgradient mapping…”
Get full text

Some Minimax Type Results Of Clarke's Generalized Directional Derivative And Point-Coderivative Of Multifunctions by Isac, G., Li, J. L.

Get full text

Primal–Dual Stability in Local Optimality by Benko, Matúš, Rockafellar, R. Tyrrell

“…Much is known about when a locally optimal solution depends in a single-valued Lipschitz continuous way on the problem’s parameters, including tilt…”
Get full text

Set-Valued Return Function and Generalized Solutions for Multiobjective Optimal Control Problems (MOC) by Guigue, A.

“…$ and provide a unique characterization for $V$ in terms of contingent derivative and coderivative for set-valued maps, which extends two previously introduced notions of generalized solution to the Hamilton--Jacobi equation for single objective…”
Get full text

Coderivative Analysis of Variational Systems by Mordukhovich, Boris S.

“… The main tools of our analysis involve coderivatives of set-valued mappings that turn out to be proper extensions of the adjoint derivative operator to nonsmooth and set-valued mappings…”
Get full text

On Lipschitz Semicontinuity Properties of Variational Systems with Application to Parametric Optimization by Uderzo, A.

“… the Fréchet coderivative of the field and the derivative of the base. Applications to the stability analysis of parametric constrained optimization problems are proposed…”
Get full text

Some Remarks on Stability of Generalized Equations by Henrion, René, Kruger, Alexander Y., Outrata, Jiří V.

“…The paper concerns the computation of the graphical derivative and the regular (Fréchet) coderivative of the solution map to a class of generalized equations, where the multivalued term amounts to the regular normal cone…”
Get full text

Characterizing Generalized Derivatives of Set-Valued Maps: Extending the Tangential and Normal Approaches by Jeffrey Pang, C. H.

“… The convexified coderivative has a bijective relationship with the set of possible generalized derivatives. We conclude by illustrating a few applications of our result. [PUBLICATION ABSTRACT]…”
Get full text

Novel theorems for the frame bundle endowed with metallic structures on an almost contact metric manifold by Khan, Mohammad Nazrul Islam

“…•The results of the derivative and coderivative of 2-form F are obtained successfully.•A theorem on Nijenhuis tensor of tensor field J˜ is proved…”
Get full text

Covering constants for metric projection operator with applications to stochastic fixed-point problems by Li, Jinlu

“…The theory of generalized differentiation in set-valued analysis is based on Mordukhovich derivative…”
Get full text

Optimality conditions for weak and firm efficiency in set-valued optimization by Durea, M.

“… We derive optimality conditions by means of the Bouligand derivative and by means of the Mordukhovich coderivative as well…”
Get full text

Mordukhovich Derivatives of Metric Projection Operator in Hilbert Spaces by Li, Jinlu

“… We find exact expressions for Mordukhovich derivatives (which are also called Mordukhovich coderivatives…”
Get full text

ZETA INVARIANTS OF MORSE FORMS by Álvarez López, Jesús A., Kordyukov, Yuri A., Leichtnam, Eric

“…$ be the induced Witten’s type perturbations of the de Rham derivative and coderivative and the Laplacian, parametrized by $z=\mu +i\nu \in \mathbb C$ ( $\mu ,\nu \in \mathbb {R}$ , $i=\sqrt {-1}$ ). Let $\zeta (s,z…”
Get full text

Second-Order Studniarski Derivatives: Computation and Application by Jelitte, Mario

“…It is known that second-order Studniarski derivatives can be used to compute tangents to the solution set of a generalized equation when standard (first-order…”
Get full text

Calculus of directional subdifferentials and coderivatives in Banach spaces by Long, Pujun, Wang, Bingwu, Yang, Xinmin

“…In this work we study the directional versions of Mordukhovich normal cones to nonsmooth sets, coderivatives of set-valued mappings, and subdifferentials of extended-real-valued functions…”
Get full text