Related papers: An operational test for existence of a consistent …
This paper studies the strong quasiconvexity of norm and distance functions in finite-dimensional normed spaces. Although the Euclidean norm is known to be strongly quasiconvex on bounded convex sets, a complete characterization of this…
We consider integration of functions with values in a partially ordered vector space, and two notions of extension of the space of integrable functions. Applying both extensions to the space of real valued simple functions on a measure…
We consider functional linear regression models where functional outcomes are associated with scalar predictors by coefficient functions with shape constraints, such as monotonicity and convexity, that apply to sub-domains of interest. To…
In this paper we prove that there exists a smooth classical solution to the HJB equation for a large class of constrained problems with utility functions that are not necessarily differentiable or strictly concave. The value function is…
We consider the space of convex functions defined in the Euclidean $n$-dimensional space, which are lower semi-continuous and tend to infinity at infinity. We study real-valued valuations defined on this space of functions, which are…
We are interested in belief revision involving conditional statements where the antecedent is almost certainly false. To represent such problems, we use Ordinal Conditional Functions that may take infinite values. We model belief change in…
We define Conditional quasi concave Performance Measures (CPMs), on random variables bounded from below, to accommodate for additional information. Our notion encompasses a wide variety of cases, from conditional expected utility and…
Theoretical developments on cross validation (CV) have mainly focused on selecting one among a list of finite-dimensional models (e.g., subset or order selection in linear regression) or selecting a smoothing parameter (e.g., bandwidth for…
There exist two major subclasses in the class of superquadratic functions, one comprises concave and decreasing functions, while the other consists of convex and monotone increasing functions. Leveraging this distinction, we introduce…
We give a sufficient condition for the strict parabolic power concavity of the convolution in space variable of a function defined on $\mathbb{R}^n \times (0,+\infty)$ and a function defined on $\mathbb{R}^n$. Since the strict parabolic…
In this paper we study an optimal portfolio selection problem under instantaneous price impact. Based on some empirical analysis in the literature, we model such impact as a concave function of the trading size when the trading size is…
The aim of this work is to certify lower bounds for real-valued multivariate functions, defined by semialgebraic or transcendental expressions. The certificate must be, eventually, formally provable in a proof system such as Coq. The…
In decision-making, maxitive functions are used for worst-case and best-case evaluations. Maxitivity gives rise to a rich structure that is well-studied in the context of the pointwise order. In this article, we investigate maxitivity with…
The aim of this paper is to present an original approach that takes advantage from the geometric features of strictly convex functions to tackle the problem of finding the minimum from another perspective. The general idea is that near the…
In decision problems under incomplete information, actions (identified to payoff vectors indexed by states of nature) and beliefs are naturally paired by bilinear duality. We exploit this duality to analyze the value of information, using…
The space of constructible functions form a dense subspace of the space of generalized valuations. In this note we prove a somewhat stronger property that the sequential closure, taken sufficiently many (in fact, infinitely many) times, of…
It is well known that functions (resp. operators) satisfying a property~$p$ on a subset $Q\subset \mathbb{R}^d$ cannot necessarily be extended to a function (resp. operator) satisfying~$p$ on the whole of~$\mathbb{R}^d$. Given $Q \subseteq…
Many computer vision and human-computer interaction applications developed in recent years need evaluating complex and continuous mathematical functions as an essential step toward proper operation. However, rigorous evaluation of this kind…
In the paper, the idea of describing not-yet-verified properties of quantum objects with logical many-valuedness is scrutinized. As it is argued, to promote such an idea, the following two foundational problems of many-valued quantum logic…
The motivation of this paper is the development of an optimisation method for solving optimisation problems appearing in Chebyshev rational and generalised rational approximation problems, where the approximations are constructed as ratios…