Radial and nonradial minimizers for some radially symmetric functionals.
Radial minimizer of a variant of the -Ginzburg-Landau functional.
Radiality and semismoothness
Random generalized set-valued strongly nonlinear implicit quasi-variational inequalities.
Random homogenization of an obstacle problem
Random perturbation of the variable metric method for unconstrained nonsmooth nonconvex optimization
We consider the global optimization of a nonsmooth (nondifferentiable) nonconvex real function. We introduce a variable metric descent method adapted to nonsmooth situations, which is modified by the incorporation of suitable random perturbations. Convergence to a global minimum is established and a simple method for the generation of suitable perturbations is introduced. An algorithm is proposed and numerical results are presented, showing that the method is computationally effective and stable....
Random variational inequalities in the absence of sample path continuity.
Rank 1 convex hulls of isotropic functions in dimension 2 by 2
Let be a rotationally invariant (with respect to the proper orthogonal group) function defined on the set of all by matrices. Based on conditions for the rank 1 convexity of in terms of signed invariants of (to be defined below), an iterative procedure is given for calculating the rank 1 convex hull of a rotationally invariant function. A special case in which the procedure terminates after the second step is determined and examples of the actual calculations are given.
Rank-one connections at infinity and quasiconvex hulls.
Rank-one-convex and quasiconvex envelopes for functions depending on quadratic forms.
Rate independent Kurzweil processes
The Kurzweil integral technique is applied to a class of rate independent processes with convex energy and discontinuous inputs. We prove existence, uniqueness, and continuous data dependence of solutions in spaces. It is shown that in the context of elastoplasticity, the Kurzweil solutions coincide with natural limits of viscous regularizations when the viscosity coefficient tends to zero. The discontinuities produce an additional positive dissipation term, which is not homogeneous of degree...
Recent advances in the analysis of pointwise state-constrained elliptic optimal control problems
Optimal control problems for semilinear elliptic equations with control constraints and pointwise state constraints are studied. Several theoretical results are derived, which are necessary to carry out a numerical analysis for this class of control problems. In particular, sufficient second-order optimality conditions, some new regularity results on optimal controls and a sufficient condition for the uniqueness of the Lagrange multiplier associated with the state constraints are presented.
Reduction by group symmetry of second order variational problems on a semidirect product of Lie groups with positive definite riemannian metric
For a riemannian structure on a semidirect product of Lie groups, the variational problems can be reduced using the group symmetry. Choosing the Levi-Civita connection of a positive definite metric tensor, instead of any of the canonical connections for the Lie group, simplifies the reduction of the variations but complicates the expression for the Lie algebra valued covariant derivatives. The origin of the discrepancy is in the semidirect product structure, which implies that the riemannian exponential...
Reduction by group symmetry of second order variational problems on a semidirect product of Lie groups with positive definite Riemannian metric
For a Riemannian structure on a semidirect product of Lie groups, the variational problems can be reduced using the group symmetry. Choosing the Levi-Civita connection of a positive definite metric tensor, instead of any of the canonical connections for the Lie group, simplifies the reduction of the variations but complicates the expression for the Lie algebra valued covariant derivatives. The origin of the discrepancy is in the semidirect product structure, which implies that the Riemannian exponential...
Reflected forward-backward SDEs and obstacle problems with boundary conditions.
Regular maximal monotone operators and the sum theorem.
Regular synthesis for the linear-convex optimal control problem with convex control constraints
Régularité de la solution d'un problème variationnel
Régularité Lipschitzienne des Géodésiques Minimisantes pour Quelques Distributions Affines
2000 Mathematics Subject Classification: 49J15, 49J30, 53B50.In the context of sub-Riemannian geometry and the Lipschitzian regularity of minimizers in control theory, we investigate some properties of minimizing geodesics for certain affine distributions. In particular, we consider the case of a generalized H2-strong affine distribution and the case of an affine Plaff system of maximal class.
Regularity and optimal control of quasicoupled and coupled heating processes
Sufficient conditions for the stresses in the threedimensional linearized coupled thermoelastic system including viscoelasticity to be continuous and bounded are derived and optimization of heating processes described by quasicoupled or partially linearized coupled thermoelastic systems with constraints on stresses is treated. Due to the consideration of heating regimes being “as nonregular as possible” and because of the well-known lack of results concerning the classical regularity of solutions...