8 research outputs found
Second-order subdifferential of 1- and maximum norm
We derive formulae for the second-order subdifferential of polyhedral norms. These formulae are fully explicit in terms of initial data. In a first step we rely on the explicit formula for the coderivative of normal cone mapping to polyhedra. Though being explicit, this formula is quite involved and difficult to apply. Therefore, we derive simple formulae for the 1-norm and -- making use of a recently obtained formula for the second-order subdifferential of the maximum function -- for the maximum norm
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Second-order subdifferential of 1- and maximum norm
We derive formulae for the second-order subdifferential of polyhedral
norms. These formulae are fully explicit in terms of initial data. In a first
step we rely on the explicit formula for the coderivative of normal cone
mapping to polyhedra. Though being explicit, this formula is quite involved
and difficult to apply. Therefore, we derive simple formulae for the 1-norm
an
Strongly stable C-stationary points for mathematical programs with complementarity constraints
In this paper we consider the class of mathematical programs with complementarity constraints (MPCC). Under an appropriate constraint qualification of Mangasarian–Fromovitz type we present a topological and an equivalent algebraic characterization of a strongly stable C-stationary point for MPCC. Strong stability refers to the local uniqueness, existence and continuous dependence of a solution for each sufficiently small perturbed problem where perturbations up to second order are allowed. This concept of strong stability was originally introduced by Kojima for standard nonlinear optimization; here, its generalization to MPCC demands a sophisticated technique which takes the disjunctive properties of the solution set of MPCC into account.publishedVersio