On directional derivatives of Skorokhod maps in convex polyhedral domains

AbstractA method will be introduced to solve problems utt — uss = h(s, t), u(t,t) - u(1+t,1 - t), u(s,0) = g(s), u(1,1) = 0 and for (s, t) in the characteristic triangle R = {(s,t) : t ≤ s ≤ 2 — t, 0 ≤ t ≤ 1}. Here represent the directional derivatives of u in the characteristic directions e1 = (— 1, — 1) and e2 = (1, — 1), respectively. The method produces the symmetric Green's function of Kreith [1] in both cases.

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Differential Games, Optimal Control and Directional Derivatives of Viscosity Solutions of Bellman’s and Isaacs’ Equations

SIAM Journal on Control and Optimization ◽

10.1137/0323036 ◽

1985 ◽

Vol 23 (4) ◽

pp. 566-583 ◽

Cited By ~ 98

Author(s):

P.-L. Lions ◽

P. E. Souganidis

Keyword(s):

Optimal Control ◽

Differential Games ◽

Viscosity Solutions ◽

Directional Derivatives ◽

Isaacs Equations ◽

Derivatives Of

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First-order and second-order ?-directional derivatives of a marginal function in convex programming with linear inequality constraints

Journal of Optimization Theory and Applications ◽

10.1007/bf00940934 ◽

1990 ◽

Vol 66 (3) ◽

pp. 489-502 ◽

Cited By ~ 2

Author(s):

S. Shiraishi

Keyword(s):

Convex Programming ◽

Linear Inequality ◽

Inequality Constraints ◽

Second Order ◽

Directional Derivatives ◽

Marginal Function ◽

First Order ◽

Linear Inequality Constraints ◽

Derivatives Of

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Second-order directional derivatives of spectral functions

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2004.11.021 ◽

2005 ◽

Vol 50 (5-6) ◽

pp. 947-955

Author(s):

S.J. Li ◽

K.L. Teo ◽

X.Q. Yang

Keyword(s):

Second Order ◽

Directional Derivatives ◽

Spectral Functions ◽

Derivatives Of

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On Derivatives and Norms of Generalized Matrix Functions and Respective Symmetric Powers

Electronic Journal of Linear Algebra ◽

10.13001/1081-3810.2850 ◽

2015 ◽

Vol 30 ◽

Cited By ~ 1

Author(s):

Sonia Carvalho ◽

Pedro Freitas

Keyword(s):

Symmetric Group ◽

Symmetric Tensor ◽

Directional Derivatives ◽

Matrix Functions ◽

Tensor Power ◽

Symmetric Powers ◽

Generalized Matrix ◽

Derivatives Of

In recent papers, S. Carvalho and P. J. Freitas obtained formulas for directional derivatives, of all orders, of the immanant and of the m-th $\xi$-symmetric tensor power of an operator and a matrix, when $\xi$ is a character of the full symmetric group. The operator bound norm of these derivatives was also calculated. In this paper similar results are established for generalized matrix functions and for every symmetric tensor power.

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