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We consider the set of points in projective $n$-space that generate an extension of degree $e$ over given number field $k$, and deduce an asymptotic formula for the number of such points of absolute height at most $X$, as $X$ tends to…
We calculate explicitly an adelic quotient group for an excellent Noetherian normal integral two-dimensional separated scheme. An application to an irreducible normal projective algebraic surface over a field is given.
This paper studies maximisation of an average-cost-per-unit-time ergodic functional over impulse strategies controlling a Feller-Markov process. The uncontrolled process is assumed to be ergodic but, unlike the extant literature, the…
We prove a $p$-adic version of the Integral Geometry Formula for averaging the intersection of two $p$-adic projective algebraic sets. We apply this result to give bounds on the number of points in the modulo $p^m$ reduction of a projective…
We propose adaptation strategies to modify the standard constrained model predictive controller scheme in order to guarantee a certain lower bound on the degree of suboptimality. Within this analysis, the length of the optimization horizon…
In this note, basing on a certain functional equation of the dilogarithm function, we establish nontrivial lower bounds for the $p$-adic valuation (where $p$ is a given prime number) of some type of rational numbers involving harmonic…
Geometric optimal control utilizes tools from differential geometry to analyze the structure of a problem to determine the control and state trajectories to reach a desired outcome while minimizing some cost function. For a controlled…
In this manuscript we study geometric regularity estimates for problems driven by fully nonlinear elliptic operators under strong absorption conditions. We establish improved geometric regularity along the free boundary, for a sharp value…
In this work, solution of the finite horizon hybrid optimal control problem as the central element of the receding horizon optimal control (model predictive control) is investigated based on the indirect approach. The response of a hybrid…
We examine the minimization of a quadratic cost functional composed of the output and the final state of abstract infinite-dimensional evolution equations in view of existence of solutions and optimality conditions. While the initial value…
Random projection is a common technique for designing algorithms in a variety of areas, including information retrieval, compressive sensing and measuring of outlyingness. In this work, the original random projection outlyingness measure is…
We consider some generalizations of the classical nonholonomic integrator and give a geometric approach to characterize controllability for these systems. We use Stokes' theorem and results from complex analysis to obtain necessary and…
The main objective of this work is to describe a general and original approach for computing an off-line solution for a set of parameters describing the geometry of the domain. That is, a solution able to include information for different…
Motivated by applications arising from sensor networks and machine learning, we consider the problem of minimizing a finite sum of nondifferentiable convex functions where each component function is associated with an agent and a…
A new exact projective penalty method is proposed for the equivalent reduction of constrained optimization problems to nonsmooth unconstrained ones. In the method, the original objective function is extended to infeasible points by summing…
In optimal control problems, there exist different kinds of extremals, that is, curves candidates to be solution: abnormal, normal and strictly abnormal. The key point for this classification is how those extremals depend on the cost…
We apply polynomial techniques (linear programming) to obtain lower and upper bounds on the covering radius of spherical designs as function of their dimension, strength, and cardinality. In terms of inner products we improve the lower…
An adaptive regularization algorithm for unconstrained nonconvex optimization is proposed that is capable of handling inexact objective-function and derivative values, and also of providing approximate minimizer of arbitrary order. In…
We apply the semidefinite programming method to derive bounds for projective codes over a finite field.
We introduce the concept of a control contraction metric, extending contraction analysis to constructive nonlinear control design. We derive sufficient conditions for exponential stabilizability of all trajectories of a nonlinear control…