Revisiting the analysis of optimal control problems with several state constraints
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 convexity.
Riemannian metric of the averaged energy minimization problem in orbital transfer with low thrust
Riemannian metrics on 2D-manifolds related to the Euler−Poinsot rigid body motion
The Euler−Poinsot rigid body motion is a standard mechanical system and it is a model for left-invariant Riemannian metrics on SO(3). In this article using the Serret−Andoyer variables we parameterize the solutions and compute the Jacobi fields in relation with the conjugate locus evaluation. Moreover, the metric can be restricted to a 2D-surface, and the conjugate points of this metric are evaluated using recent works on surfaces of revolution. Another related 2D-metric on S2 associated to the...
Rigidity for the hyperbolic Monge-Ampère equation
Some properties of nonlinear partial differential equations are naturally associated with the geometry of sets in the space of matrices. In this paper we consider the model case when the compact set is contained in the hyperboloid , where , the set of symmetric matrices. The hyperboloid is generated by two families of rank-one lines and related to the hyperbolic Monge-Ampère equation . For some compact subsets containing a rank-one connection, we show the rigidity property of by imposing...
Rilassamento e fenomeno di Lavrentiev per alcune classi di funzionali integrali
Robinson's implicit function theorem
Robust control problems of vortex dynamics in superconducting films with Ginzburg-Landau complex systems.
Robust portfolio selection under exponential preferences
We consider an incomplete market with an untradable stochastic factor and a robust investment problem based on the CARA utility. We formulate it as a stochastic differential game problem, and use Hamilton-Jacobi-Bellman-Isaacs equations to derive an explicit representation of the robust optimal portfolio; the HJBI equation is transformed using a substitution of the Cole-Hopf type. Not only the pure investment problem, but also a problem of robust hedging is taken into account: an agent tries to...
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...
Rotating drops in a vessel. Existence of local minima
Rotating drops trapped between parallel planes
Rotationally invariant periodic solutions of semilinear wave equations.
Rothe approach to the existence of solution of an ablation-transpiration cooling control system.
Rotundity, smoothness and duality