Linear-quadratic optimization and some general hypotheses on optimal control.
Links between young measures associated to constrained sequences
Links between Young measures associated to constrained sequences
We give necessary and sufficient conditions which characterize the Young measures associated to two oscillating sequences of functions, un on and vn on satisfying the constraint . Our study is motivated by nonlinear effects induced by homogenization. Techniques based on equimeasurability and rearrangements are employed.
Lipschitz continuity of the state function in a shape optimization problem.
Lipschitz Continuous Solutions for Nonlinear Obstacle Problems.
Lipschitz functions with unexpectedly large sets of nondifferentiability points.
Lipschitz mappings, contingents, and differentiability.
Lipschitz modulus in convex semi-infinite optimization via d.c. functions
We are concerned with the Lipschitz modulus of the optimal set mapping associated with canonically perturbed convex semi-infinite optimization problems. Specifically, the paper provides a lower and an upper bound for this modulus, both of them given exclusively in terms of the problem’s data. Moreover, the upper bound is shown to be the exact modulus when the number of constraints is finite. In the particular case of linear problems the upper bound (or exact modulus) adopts a notably simplified...
Lipschitz modulus in convex semi-infinite optimization via d.c. functions
We are concerned with the Lipschitz modulus of the optimal set mapping associated with canonically perturbed convex semi-infinite optimization problems. Specifically, the paper provides a lower and an upper bound for this modulus, both of them given exclusively in terms of the problem's data. Moreover, the upper bound is shown to be the exact modulus when the number of constraints is finite. In the particular case of linear problems the upper bound (or exact modulus) adopts a notably simplified...
Lipschitz regularity for some asymptotically convex problems
We establish a local Lipschitz regularity result for local minimizers of asymptotically convex variational integrals.
Lipschitz regularity for some asymptotically convex problems*
We establish a local Lipschitz regularity result for local minimizers of asymptotically convex variational integrals.
Lipschitz stability of optimal controls for the steady-state Navier-Stokes equations
Lipschitz stability of solutions to parametric optimal control problems for parabolic equations.
Lipschitzian generalized differential equations
Liquid crystals : relaxed energies, dipoles, singular lines and singular points
L∞-Norm minimal control of the wave equation: on the weakness of the bang-bang principle
For optimal control problems with ordinary differential equations where the -norm of the control is minimized, often bang-bang principles hold. For systems that are governed by a hyperbolic partial differential equation, the situation is different: even if a weak form of the bang-bang principle still holds for the wave equation, it implies no restriction on the form of the optimal control. To illustrate that for the Dirichlet boundary control of the wave equation in general not even feasible...
Local analysis of a cubically convergent method for variational inclusions
This paper deals with variational inclusions of the form 0 ∈ φ(x) + F(x) where φ is a single-valued function admitting a second order Fréchet derivative and F is a set-valued map from to the closed subsets of . When a solution z̅ of the previous inclusion satisfies some semistability properties, we obtain local superquadratic or cubic convergent sequences.
Local boundedness of minimizers of anisotropic functionals
Local Boundedness of minimzers in a limit case.
Local calibrations for minimizers of the Mumford–Shah functional with a regular discontinuity set