Méthode du sous-gradient réduit généralisé comme extension du GRG d'Abadie au cas non différentiable
Metric subregularity for nonclosed convex multifunctions in normed spaces
In terms of the normal cone and the coderivative, we provide some necessary and/or sufficient conditions of metric subregularity for (not necessarily closed) convex multifunctions in normed spaces. As applications, we present some error bound results for (not necessarily lower semicontinuous) convex functions on normed spaces. These results improve and extend some existing error bound results.
Minimal invasion: An optimal L∞ state constraint problem
In this work, the least pointwise upper and/or lower bounds on the state variable on a specified subdomain of a control system under piecewise constant control action are sought. This results in a non-smooth optimization problem in function spaces. Introducing a Moreau-Yosida regularization of the state constraints, the problem can be solved using a superlinearly convergent semi-smooth Newton method. Optimality conditions are derived, convergence of the Moreau-Yosida regularization is proved, and...
Minimal invasion: An optimal L∞ state constraint problem
In this work, the least pointwise upper and/or lower bounds on the state variable on a specified subdomain of a control system under piecewise constant control action are sought. This results in a non-smooth optimization problem in function spaces. Introducing a Moreau-Yosida regularization of the state constraints, the problem can be solved using a superlinearly convergent semi-smooth Newton method. Optimality conditions are derived, convergence of the Moreau-Yosida regularization is proved, and...
Minimal pairs representing selections of four linear functions in .
Minimization of nonsmooth convex functionals in Banach spaces.
Minimization of nonsmooth integral functionals.
Monotone trajectories of dynamical systems and Clarke's generalized Jacobian.
Monotonicity and differential properties of the value functions in optimal control.
More than first-order developments of convex functions: primal-dual relations.
Moreau's decomposition theorem revisited
Multiple solutions for a singular semilinear elliptic problems with critical exponent and symmetries.
Multivalued backward stochastic differential equations with time delayed generators
Our aim is to study the following new type of multivalued backward stochastic differential equation: where ∂φ is the subdifferential of a convex function and (Y t, Z t):= (Y(t + θ), Z(t + θ))θ∈[−T,0] represent the past values of the solution over the interval [0, t]. Our results are based on the existence theorem from Delong Imkeller, Ann. Appl. Probab., 2010, concerning backward stochastic differential equations with time delayed generators.