Related papers: Optimality conditions for an exhausterable functio…
This paper develops a novel approach to necessary optimality conditions for constrained variational problems defined in generally incomplete subspaces of absolutely continuous functions. Our approach involves reducing a variational problem…
Set- and vector-valued optimization problems can be re-formulated as complete lattice-valued problems. This has several advantages, one of which is the existence of a clear-cut solution concept which includes the attainment as the infimum…
We investigate the existence of approximation algorithms for maximization of submodular functions, that run in fixed parameter tractable (FPT) time. Given a non-decreasing submodular set function $v: 2^X \to \mathbb{R}$ the goal is to…
The geometric problem of estimating an unknown compact convex set from evaluations of its support function arises in a range of scientific and engineering applications. Traditional approaches typically rely on estimators that minimize the…
We study a relationship between rational proper maps of balls in different dimensions and strongly plurisubharmonic exhaustion functions of the unit ball induced by such maps. Putting the unique critical point of this exhaustion function at…
In this paper we study the radial epiderivative notion for nonconvex functions, which extends the (classical) directional derivative concept. The paper presents new definition and new properties for this notion and establishes relationships…
Many researchers in artificial intelligence are beginning to explore the use of soft constraints to express a set of (possibly conflicting) problem requirements. A soft constraint is a function defined on a collection of variables which…
This manuscript introduces the idea of GS-exponential kind of convex functions and some of their algebraic features, and we introduce a new class GS-exponential kind of convex sets. In addition, we describe certain fundamental…
Via a family of monotone scalar functions, a preorder on a set is extended to its power set and then used to construct a hull operator and a corresponing complete lattice of sets. A function mappping into the preordered set is extended to a…
We propose a general method for optimization with semi-infinite constraints that involve a linear combination of functions, focusing on the case of the exponential function. Each function is lower and upper bounded on sub-intervals by…
Submodular set-functions have many applications in combinatorial optimization, as they can be minimized and approximately maximized in polynomial time. A key element in many of the algorithms and analyses is the possibility of extending the…
We define w-invex set, w-preinvex, w-strictly preinvex, w-quasi preinvex, w-strictly quasi preinvex, w-semi-strictly quasi preinvex, and w-pre pseudo-invex functions in this context. And these form a class of real functions, which is the…
This paper investigates the possibility of constructive extraction of measurable selector from set-valued maps which may commonly arise in viability theory, optimal control, discontinuous systems etc. For instance, existence of solutions to…
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…
We consider convex sets and functions over idempotent semifields, like the max-plus semifield. We show that if $K$ is a conditionally complete idempotent semifield, with completion $\bar{K}$, a convex function $K^n\to\bar{K}$ which is lower…
We establish explicit data-dependent and symmetric characterizations of the subdifferential of the supremum of convex functions, formulated directly in terms of the underlying data functions. In our approach, both active and non-active…
This paper is concerned with necessary and sufficient second-order conditions for finite-dimensional and infinite-dimensional constrained optimization problems. Using a suitably defined directional curvature functional for the admissible…
This paper investigates the behavior of sets and functions at infinity by introducing new concepts, namely directional normal cones at infinity for unbounded sets, along with limiting and singular subdifferentials at infinity in the…
We define the supermodular rank of a function on a lattice. This is the smallest number of terms needed to decompose it into a sum of supermodular functions. The supermodular summands are defined with respect to different partial orders. We…
We develop refined Karush-Kuhn-Tucker (KKT) and Fritz-John (FJ)-type optimality conditions for nonsmooth, nonconvex mathematical pro\-gra\-mming problems. We pay special attention in the case that the functional constraint belongs to a…