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In the propositional setting, the marginal problem is to find a (maximum-entropy) distribution that has some given marginals. We study this problem in a relational setting and make the following contributions. First, we compare two…
Motivated by the study of systems of higher order boundary value problems with functional boundary conditions, we discuss, by topological methods, the solvability of a fairly general class of systems of perturbed Hammerstein integral…
In this paper we consider a boundary value problem for fully fourth order nonlinear functional differential equation which contains all lower derivatives of proportional delay arguments. By the reduction of the problem to operator equation…
Taking the Fourier integral theorem as our starting point, in this paper we focus on natural Monte Carlo and fully nonparametric estimators of multivariate distributions and conditional distribution functions. We do this without the need…
The classical multivariate extreme-value theory concerns the modeling of extremes in a multivariate random sample, suggesting the use of max-stable distributions. In this work, the classical theory is extended to the case where aggregated…
We study an optimal control problem in which both the objective function and the dynamic constraint contain an uncertain parameter. Since the distribution of this uncertain parameter is not exactly known, the objective function is taken as…
In this paper a class of optimization problems with uncertain linear constraints is discussed. It is assumed that the constraint coefficients are random vectors whose probability distributions are only partially known. Possibility theory is…
We study a general class of functionals providing an analytic handle on the conformal bootstrap equations in one dimension. We explicitly identify the extremal functionals, corresponding to theories saturating conformal bootstrap bounds, in…
We address the issue of semiparametric efficiency in the bivariate regression problem with a highly persistent predictor, where the joint distribution of the innovations is regarded an infinite-dimensional nuisance parameter. Using a…
We place ourselves in a functional regression setting and propose a novel methodology for regressing a real output on vector-valued functional covariates. This methodology is based on the notion of signature, which is a representation of a…
This paper presents the first study of the complexity of the optimization problem for integer linear-exponential programs which extend classical integer linear programs with the exponential function $x \mapsto 2^x$ and the remainder…
We study fractional variational problems of Herglotz type of variable order. Necessary optimality conditions, described by fractional differential equations depending on a combined Caputo fractional derivative of variable order, are proved.…
We solve two continuous extremal problems on the classes of monotone functions: in the first problem we find extremal values for a line integral of a coordinate-wise monotone function of two variables from a rearrange\-ment-invariant class…
In this paper we study the right differentiability of a parametric infimum function over a parametric set defined by equality constraints. We present a new theorem with sufficient conditions for the right differentiability with respect to…
It is a longstanding unsolved problem to characterize the optimal feedback controls for general linear quadratic optimal control problem of stochastic evolution equation with random coefficients. A solution to this problem is given in [21]…
The paper studies generalized differentiability properties of the marginal function of parametric optimal control problems of semilinear elliptic partial differential equations. We establish upper estimates for the regular and the limiting…
Necessary optimality conditions and numerical methods for solving an optimal control problem for a linear continuous-time dynanical system with controlled coefficients and quadratic goal functional are discussed.
Numerical solving differential equations with fractional derivatives requires elimination of the singularity which is inherent in the standard definition of fractional derivatives. The method of integration by parts to eliminate this…
We consider a one dimensional elliptic distributed optimal control problem with pointwise constraints on the derivative of the state. By exploiting the variational inequality satisfied by the derivative of the optimal state, we obtain…
Optimization under uncertainty deals with the problem of optimizing stochastic cost functions given some partial information on their inputs. These problems are extremely difficult to solve and yet pervade all areas of technological and…