On proto-differentiability of generalized perturbation maps
https://doi.org/10.1016/j.jmaa.2006.01.030Publisher, magazine: ,
Publication year: 2006
Lưu Trích dẫn Chia sẻAbstract
Main result: Under some suitable qualification conditions, the generalized perturbation map \(G\) (that is, the solution set map to a parameterized constraint system, to a parameterized variational inequality, or to a parameterized optimization problem) in \(G(x,z)=\{ y\in D: z\in F(x,y)+K(y)\}\) (where \(F:R^d\times R^n = R^m , K: R^n = R^m)\) is proto-differentiable. The precise proofs of the main results are proposed.
Tags: optimization; variational inequality; Fréchet differentiable function; closed convex subset in \(R^n\); contingent cone; adjacent cone; multifunction; perturbation map; proto-differentiability
Các bài viết liên quan đến tác giả Gue Myung Lee
Efficiency and generalised convexity in vector optimisation problems
Hartley Proper Efficiency in Multifunction Optimization
Infine functions, nonsmooth alternative theorems and vector optimization problems.
Characterizations of Hartley proper efficiency in nonconvex vector optimization
On the optimal value function of a linearly perturbed quadratic program
Sequential Lagrangian conditions for convex programs with applications to semidefinite programming
Some remarks on the elliptic regularization method
On Monotone and Strongly Monotone Vector Variational Inequalities