In this article we analyze the optimal control strategy for rotating a monitored qubit from an initial pure state to an orthogonal state in minimum time. This strategy is described for two different cost functions of interest which do not have the usual regularity properties. Hence, as classically smooth cost functions may not exist, we interpret these functions as viscosity solutions to the op...

We consider a non-stationary sequential stochastic optimization problem, in which the underlying cost functions change over time under a variation budget constraint. We propose an Lp,q-variation functional to quantify the change, which captures local spatial and temporal variations of the sequence of functions. Under the Lp,q-variation functional constraint, we derive both upper and matching lo...

As recently discussed by Bar, Kiryati, and Sochen in [3], the Ambrosio-Tortorelli approximation of the Mumford-Shah functional defines an extended line process regularization where the regularizer has an additional constraint introduced by the term ρ|∇v|. This term mildly forces some spatial organization by demanding that the edges are smooth. However, it does not force spatial coherence such a...

This paper deals with the optimization of a hydrothermal problem that considers a non-smooth Lagrangian L(t, z, z′). We consider a general case where the functions Lz′ (t, ·, ·) and Lz(t, ·, ·) are discontinuous in {(t, z, z′)/z′ = φ(t, z)}, which is the borderline point between two power generation zones. This situation arises in problems of optimization of hydrothermal systems where the therm...

A parametric version of the Borwein-Preiss smooth variational principle is presented, which states that under suitable assumptions on a given convex function depending on a parameter, the minimum point of a smooth convex perturbation of it depends continuously on the parameter. Some applications are given: existence of a Nash equilibrium and a solution of a variational inequality for a system o...

In non-rigid image registration problems, it can be difficult to construct a single cost function that adequately captures concepts of similarity for multiple structures, for example when one structure changes in density while another structure does not. We propose a method that locally switches between cost functions at each iteration of the registration process. This allows more specific simi...

We propose an alternative method for computing e¤ectively the solution of the control inventory problem under non-convex polynomial cost functions. We apply the method of moments in global optimization to transform the corresponding, non-convex dynamic programming problem into an equivalent optimal control problem with linear and convex structure. We device computational tools based on convex o...

A Tsallis-statistics-based generalization of the gradient descent dynamics (using non- extensive cost functions), recently introduced by one of us, is proposed as a learning rule in a simple perceptron. The resulting Langevin equations are solved numerically for different values of an index q (q = 1 and q ≠ 1 respectively correspond to the extensive and non-extensive cases) and for different co...

We study the backfitting and profile methods for general criterion functions that depend on a parameter of interest β and a nuisance function θ. We show that when different amounts of smoothing are employed for each method to estimate the function θ, the two estimation procedures produce asymptotically the same estimator of β, even when the criterion functions are non-smooth in β and/or θ. The ...

In this paper we will extend the input-to-state stability (ISS) framework introduced by Sontag to continuous-time discontinuous dynamical systems adopting Filippov’s solution concept and using non-smooth ISS Lyapunov functions. The main motivation for investigating non-smooth ISS Lyapunov functions is the recent focus on “multiple Lyapunov functions” for which feasible computational schemes are...