相关论文: Constructing the demand function of a strictly con…

In this manuscript, we consider a control system governed by a general ordinary differential equation on a Riemannian manifold, with its endpoints satisfying some inequalities and equalities, and its control constrained to a closed convex…

The main result states that every convex set-valued function defined on a real interval with compact values in a locally convex space, admits an affine selection. In the case if the target space is a real line and the values are closed real…

Choice functions accept a set of alternatives as input and produce a preferred subset of these alternatives as output. We study the problem of learning such functions under conditions of context-dependence of preferences, which means that…

We provide a necessary and sufficient condition for rationalizable implementation of social choice functions, i.e., we offer a complete answer regarding what social choice functions can be rationalizably implemented.

In information theory, some optimization problems result in convex optimization problems on strictly convex functionals of probability densities. In this note, we study these problems and show conditions of minimizers and the uniqueness of…

We apply the Weber-Fechner's law, which represents the relation between the magnitude of physical stimulus and the magnitude of psychological sense in human being, to the utility function. We conclude that the utility function of n-types of…

We tackle the problem of constructive preference elicitation, that is the problem of learning user preferences over very large decision problems, involving a combinatorial space of possible outcomes. In this setting, the suggested…

In order to alleviate the inefficiencies caused by the interaction of the logic and functional sides, integrated languages may take advantage of \emph{demand} information -- i.e. knowing in advance which computations are needed and, to…

We present a non-linear inequality that completely characterizes the set of correlation functions obtained from bipartite quantum systems, for the case in which measurements on each subsystem can be chosen between two arbitrary dichotomic…

Sequential decision-making is desired to align with human intents and exhibit versatility across various tasks. Previous methods formulate it as a conditional generation process, utilizing return-conditioned diffusion models to directly…

We consider a stochastic control problem where the set of strict (classical) controls is not necessarily convex, and the system is governed by a nonlinear backward stochastic differential equation. By introducing a new approach, we…

We exploit qualitative probabilistic relationships among variables for computing bounds of conditional probability distributions of interest in Bayesian networks. Using the signs of qualitative relationships, we can implement abstraction…

Extension problems for polynomial valuations on different cones of convex functions are investigated. It is shown that for the classes of functions under consideration, the extension problem reduces to a simple geometric obstruction on the…

We give an elementary proof of a somewhat curious result, namely, that deciding whether a convex function is self-concordant is in general an intractable problem.

We give a sharp convexity estimate for L-functions which have a functional equation and an Euler product.

Multimodular functions, primarily used in the literature of queueing theory, discrete-event systems, and operations research, constitute a fundamental function class in discrete convex analysis. The objective of this paper is to clarify the…

The paper is devoted to obtain first and second order necessary optimality conditions for continuous-time optimization problems with equality and inequality constraints. A full rank type regularity condition along with an uniform implicit…

A recipe is presented for constructing band-limited superoscillating functions that exhibit arbitrarily high frequencies over arbitrarily long intervals.

Literature involving preferences of artificial agents or human beings often assume their preferences can be represented using a complete transitive binary relation. Much has been written however on different models of preferences. We review…

Dependence on the parameter is continuous when perturbations of the parameter preserves strict preference for one alternative over another. We characterise this property via a utility function over alternatives that depends continuously on…