Related papers: A Note on Ordinally Concave Functions
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-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…
Functions with uniform sublevel sets can represent orders, preference relations or other binary relations and thus turn out to be a tool for scalarization that can be used in multicriteria optimization, decision theory, mathematical…
In this note we investigate the inclusion relationship between the class of strongly starlike functions of order alpha and type beta and the class of strongly convex functions of order alpha and type beta which are subclass of normalized…
The concepts of amenable and compatible functions have been introduced in a recent work, in order to state precise mathematical theorems that guarantee that a backward stable algorithm is also forward stable, and that the composition of two…
We investigate expected utility maximization problems from the terminal liquidation value in continuous time in markets with transaction costs and one fixed consistent price system, where a non-concave utility function is defined on the…
Perhaps, it is not too far from the truth to say that, among the great concepts (as compactness, completeness, order, convexity) on which functional analysis is based, connectedness is relatively less popular, though this does not mean that…
Given an initial matching and a policy objective on the distribution of agent types to institutions, we study the existence of a mechanism that weakly improves the distributional objective and satisfies constrained efficiency, individual…
Many convex optimization problems have structured objective function written as a sum of functions with different types of oracles (full gradient, coordinate derivative, stochastic gradient) and different evaluation complexity of these…
We study minimization of a structured objective function, being the sum of a smooth function and a composition of a weakly convex function with a linear operator. Applications include image reconstruction problems with regularizers that…
Recently classes of conic and discrete conic functions were introduced. In this paper we use the term convic instead conic. The class of convic functions properly includes the classes of convex functions, strictly quasiconvex functions and…
We propose a new class of convex penalty functions, called \emph{variational Gram functions} (VGFs), that can promote pairwise relations, such as orthogonality, among a set of vectors in a vector space. These functions can serve as…
Functions with uniform level sets can represent orders, preference relations or other binary relations and thus turn out to be a tool for scalarization that can be used, e.g., in multicriteria optimization, decision theory, mathematical…
We introduce the notion of orbital L-functions for the space of binary cubic forms and investigate their analytic properties. We study their functional equations and residue formulas in some detail. Aside from the intrinsic interest,…
We define the functional LYZ ellipsoid of log-concave functions. Then we give notes appended to [6].
We analyze matrix convex functions of a fixed order defined on a real interval by differential methods as opposed to the characterization in terms of divided differences given by Kraus. We obtain for each order conditions for matrix…
This paper studies the convexity properties of nonsmooth extended-real-valued weakly convex functions, a class of functions that is central to modern optimization and its applications. We establish new characterizations of convexity using…
We determine sufficient conditions under which certain recursively defined functions are well defined for all real inputs. Given a function $f:\mathbb R\to\mathbb R$, call a decreasing sequence $x_1>x_2>x_3>\cdots$ "$f$-bad" if…
We consider an optimization problem with positively homogeneous functions in its objective and constraint functions. Examples of such positively homogeneous functions include the absolute value function and the $p$-norm function, where $p$…
We introduce a new class of functions that can be minimized in polynomial time in the value oracle model. These are functions $f$ satisfying $f(x)+f(y)\ge f(x \sqcap y)+f(x \sqcup y)$ where the domain of each variable $x_i$ corresponds to…