Elastic knots in euclidean 3-space
Employing different loss functions for the classification of images via supervised learning
Supervised learning methods are powerful techniques to learn a function from a given set of labeled data, the so-called training data. In this paper the support vector machines approach is applied to an image classification task. Starting with the corresponding Tikhonov regularization problem, reformulated as a convex optimization problem, we introduce a conjugate dual problem to it and prove that, whenever strong duality holds, the function to be learned can be expressed via the dual optimal solutions....
Ensembles quasiminimaux pour le périmètre avec contrainte de volume et rectificabilité uniforme
Epi-distance convergence of parametrised sums of convex functions in non-reflexive spaces.
Epi/hypo-convergence: The slice topology and saddle points approximation.
Equivalent cost functionals and stochastic linear quadratic optimal control problems
This paper is concerned with the stochastic linear quadratic optimal control problems (LQ problems, for short) for which the coefficients are allowed to be random and the cost functionals are allowed to have negative weights on the square of control variables. We propose a new method, the equivalent cost functional method, to deal with the LQ problems. Comparing to the classical methods, the new method is simple, flexible and non-abstract. The new method can also be applied to deal with nonlinear...
Ergodic control of linear stochastic equations in a Hilbert space with fractional Brownian motion
A linear-quadratic control problem with an infinite time horizon for some infinite dimensional controlled stochastic differential equations driven by a fractional Brownian motion is formulated and solved. The feedback form of the optimal control and the optimal cost are given explicitly. The optimal control is the sum of the well known linear feedback control for the associated infinite dimensional deterministic linear-quadratic control problem and a suitable prediction of the adjoint optimal system...
Erratum for higher-order weakly generalized adjacent epiderivatives and applications to duality of set-valued optimization.
Error bounds for convex constrained systems in Banach spaces
Error estimate for optimality of distributed parameter control problems via duality.
Error estimates for the finite element discretization of semi-infinite elliptic optimal control problems
In this paper we derive a priori error estimates for linear-quadratic elliptic optimal control problems with finite dimensional control space and state constraints in the whole domain, which can be written as semi-infinite optimization problems. Numerical experiments are conducted to ilustrate our theory.
Everywhere regularity for a class of elliptic systems without growth conditions
Everywhere regularity for vectorial functionals with general growth
We prove Lipschitz continuity for local minimizers of integral functionals of the Calculus of Variations in the vectorial case, where the energy density depends explicitly on the space variables and has general growth with respect to the gradient. One of the models iswith a convex function with general growth (also exponential behaviour is allowed).
Everywhere regularity for vectorial functionals with general growth
We prove Lipschitz continuity for local minimizers of integral functionals of the Calculus of Variations in the vectorial case, where the energy density depends explicitly on the space variables and has general growth with respect to the gradient. One of the models is with h a convex function with general growth (also exponential behaviour is allowed).
Examples from the calculus of variations. I. Nondegenerate problems
The criteria of extremality for classical variational integrals depending on several functions of one independent variable and their derivatives of arbitrary orders for constrained, isoperimetrical, degenerate, degenerate constrained, and so on, cases are investigated by means of adapted Poincare-Cartan forms. Without ambitions on a noble generalizing theory, the main part of the article consists of simple illustrative examples within a somewhat naive point of view in order to obtain results resembling...
Examples from the calculus of variations. II. A degenerate problem
Continuing the previous Part I, the degenerate first order variational integrals depending on two functions of one independent variable are investigated.
Existence and regularity of minima for integral functionals noncoercive in the energy space
Existence and regularity of minimizers of nonconvex integrals with p-q growth
We show that local minimizers of functionals of the form , , are locally Lipschitz continuous provided f is a convex function with growth satisfying a condition of qualified convexity at infinity and g is Lipschitz continuous in u. As a consequence of this, we obtain an existence result for a related nonconvex functional.
Existence and regularity of optimal solution for a dead oil isotherm problem.
Existence and uniqueness for optimal control of oxygen absorption in aquatic system.