Regularity properties of optimal segmentations.
Regularity properties of optimal transportation problems arising in hedonic pricing models
We study a form of optimal transportation surplus functions which arise in hedonic pricing models. We derive a formula for the Ma–Trudinger–Wang curvature of these functions, yielding necessary and sufficient conditions for them to satisfy (A3w). We use this to give explicit new examples of surplus functions satisfying (A3w), of the form b(x,y) = H(x + y) where H is a convex function on ℝn. We also show that the distribution of equilibrium contracts in this hedonic pricing model is absolutely continuous...
Regularity results for a class of obstacle problems
We prove some optimal regularity results for minimizers of the integral functional belonging to the class , where is a fixed function, under standard growth conditions of -type, i.e.
Regularity results for a class of quasiconvex functionals with nonstandard growth
Regularity results for an optimal design problem with a volume constraint
Regularity results for minimal configurations of variational problems involving both bulk and surface energies and subject to a volume constraint are established. The bulk energies are convex functions with p-power growth, but are otherwise not subjected to any further structure conditions. For a minimal configuration (u,E), Hölder continuity of the function u is proved as well as partial regularity of the boundary of the minimal set E. Moreover, full regularity of the boundary of the minimal set...
Regularity results for anisotropic image segmentation models
Regularization and iterative methods for monotone variational inequalities.
Regularization parameter selection in discrete ill-posed problems - the use of the U-curve
To obtain smooth solutions to ill-posed problems, the standard Tikhonov regularization method is most often used. For the practical choice of the regularization parameter α we can then employ the well-known L-curve criterion, based on the L-curve which is a plot of the norm of the regularized solution versus the norm of the corresponding residual for all valid regularization parameters. This paper proposes a new criterion for choosing the regularization parameter α, based on the so-called U-curve....
Remarks about energy transfer in an RC ladder network
The problem of energy transfer in an -ladder network is considered. Using the maximum principle, an algorithm for constructing optimal control is proposed, where the cost function is the energy delivered to the network. In the case considered, optimal control exists. Numerical simulations were performed using Matlab.
Remarks on regularity up to the boundary for solutions to variational problems in plasticity theory
Removable singularities for bounded -harmonic functions and quasi(super)harmonic functions.
Representation formulas for L∞ norms of weakly convergent sequences of gradient fields in homogenization
We examine the composition of the L∞ norm with weakly convergent sequences of gradient fields associated with the homogenization of second order divergence form partial differential equations with measurable coefficients. Here the sequences of coefficients are chosen to model heterogeneous media and are piecewise constant and highly oscillatory. We identify local representation formulas that in the fine phase limit provide upper bounds on the limit superior of the L∞ norms of gradient fields. The...
Representation formulas for L∞ norms of weakly convergent sequences of gradient fields in homogenization
We examine the composition of the L∞ norm with weakly convergent sequences of gradient fields associated with the homogenization of second order divergence form partial differential equations with measurable coefficients. Here the sequences of coefficients are chosen to model heterogeneous media and are piecewise constant and highly oscillatory. We identify local representation formulas that in the fine phase limit provide upper bounds on the limit...
Resonance of minimizers for n-level quantum systems with an arbitrary cost
We consider an optimal control problem describing a laser-induced population transfer on a -level quantum system. For a convex cost depending only on the moduli of controls (i.e. the lasers intensities), we prove that there always exists a minimizer in resonance. This permits to justify some strategies used in experimental physics. It is also quite important because it permits to reduce remarkably the complexity of the problem (and extend some of our previous results for and ): instead of looking...
Resonance of minimizers for n-level quantum systems with an arbitrary cost
We consider an optimal control problem describing a laser-induced population transfer on a n-level quantum system. For a convex cost depending only on the moduli of controls (i.e. the lasers intensities), we prove that there always exists a minimizer in resonance. This permits to justify some strategies used in experimental physics. It is also quite important because it permits to reduce remarkably the complexity of the problem (and extend some of our previous results for n=2 and n=3): instead...
Revisiting the construction of gap functions for variational inequalities and equilibrium problems via conjugate duality
Based on conjugate duality we construct several gap functions for general variational inequalities and equilibrium problems, in the formulation of which a so-called perturbation function is used. These functions are written with the help of the Fenchel-Moreau conjugate of the functions involved. In case we are working in the convex setting and a regularity condition is fulfilled, these functions become gap functions. The techniques used are the ones considered in [Altangerel L., Boţ R.I., Wanka...
Riemannian metric of the averaged energy minimization problem in orbital transfer with low thrust
Robust real-time optimization for the linear oil blending
In this paper we present a robust real-time optimization method for the online linear oil blending process. The blending process consists in determining the optimal mix of components so that the final product satisfies a set of specifications. We examine different sources of uncertainty inherent to the blending process and show how to address this uncertainty applying the Robust Optimization techniques. The polytopal structure of our problem permits a simplified robust approach. Our method is intended...
Rotundity, smoothness and duality