One of the main difficulties in nonsmooth analysis is to devise calculus rules. It is our purpose here to show that a certain cooperative behavior between functions (resp. sets, resp. multifunctions) yields calculus r...
详细信息
One of the main difficulties in nonsmooth analysis is to devise calculus rules. It is our purpose here to show that a certain cooperative behavior between functions (resp. sets, resp. multifunctions) yields calculus rules for subdifferentials (resp. normal cones, resp. coderivatives). In previous contributions, the qualification conditions ensuring calculus rules were given in a non symmetric way. The new conditions can be combined easily and encompass various criteria. We also address the important question of the extension of calculus rules from the Lipschitz case to the general case.
This paper establishes a simple and easily-applied criterion for determining whether a multivalued mapping is metrically regular relatively to a subset in the range space.
This paper establishes a simple and easily-applied criterion for determining whether a multivalued mapping is metrically regular relatively to a subset in the range space.
The paper gives sufficient conditions for local reachability and local controllability in the following discrete-time dynamical system xk+1∈Fk(xk) (k = 0, 1, ..., K - 1) with phase constraints xk∈Mk (k = 1, 2, ..., ...
详细信息
Directional compactness, scalarization and nonsmooth semi-Fredholm mappings are explored. It is shown that with the limiting subdifferentials both the scalarization formula and the point regularity criterion hold for ...
详细信息
Directional compactness, scalarization and nonsmooth semi-Fredholm mappings are explored. It is shown that with the limiting subdifferentials both the scalarization formula and the point regularity criterion hold for Lipschitz mapping between finite dimensional spaces. The scalarization formula for directionally compact mappings is proved. The class of semi-Fredholm mappings is introduce by using a stronger form of directional compactness and show that the mappings and certain associated set-valued mappings do have the codirectional compactness property.
We show that in two dimensions or higher, the Mordukhovich-Ioffe approximate subdifferential and Clarke subdifferential may differ almost everywhere for real-valued Lipschitz functions. Uncountably many Frechet differ...
详细信息
We show that in two dimensions or higher, the Mordukhovich-Ioffe approximate subdifferential and Clarke subdifferential may differ almost everywhere for real-valued Lipschitz functions. Uncountably many Frechet differentiable vector-valued Lipschitz functions differing by more than constants can share the same Mordukhovich-Ioffe coderivatives. Moreover, the approximate Jacobian associated with the Mordukhovich-Ioffe coderivative can be nonconvex almost everywhere for Frechet differentiable vector-valued Lipschitz functions. Finally we show that for vector-valued Lipschitz functions the approximate Jacobian associated with the Mordukhovich-Ioffe coderivative can be almost everywhere disconnected.
暂无评论