相关论文: Existence and uniqueness of maximal elements for p…
We introduce the notion of weak minimizer in set optimization. Necessary and sufficient conditions in terms of scalarized variational inequalities of Stampacchia and Minty type, respectively, are proved. As an application, we obtain…
We extend Berge's Maximum Theorem to allow for incomplete preferences. We first provide a simple version of the Maximum Theorem for convex feasible sets and a fixed preference. Then, we show that if, in addition to the traditional…
We present a new elementary proof of the existence of the least and the greatest solutions to initial value problems in the conditions of Peano's existence theorem. Our proof is based on a modification of Perron's method which allows us to…
Extremal problems are studied involving an objective function with values in (order) complete lattices of sets generated by so called set relations. Contrary to the popular paradigm in vector optimization, the solution concept for such…
We study necessary and sufficient conditions to attain solutions of set-optimization problems in therms of variational inequalities of Stampacchia and Minty type. The notion of a solution we deal with has been introduced Heyde and Loehne,…
We consider methods for aggregating preferences that are based on the resolution of discrete optimization problems. The preferences are represented by arbitrary binary relations (possibly weighted) or incomplete paired comparison matrices.…
Maximizing monotone submodular functions under cardinality constraints is a classic optimization task with several applications in data mining and machine learning. In this paper we study this problem in a dynamic environment with…
We present a new optimization-based method for aggregating preferences in settings where each voter expresses preferences over pairs of alternatives. Our approach to identifying a consensus partial order is motivated by the observation that…
We prove some new results on existence of solutions to first--order ordinary differential equations with deviating arguments. Delay differential equations are included in our general framework, which even allows deviations to depend on the…
The element distinctness problem is the problem of determining whether the elements of a list are distinct, that is, if $x=(x_1,...,x_N)$ is a list with $N$ elements, we ask whether the elements of $x$ are distinct or not. The solution in a…
Since the seminal papers by Giannessi, an interesting topic in vector optimization has been the characterization of (weak) efficiency thorough Minty and Stampacchia type variational inequalities. Several results have been proved to extend…
In this paper, we construct and compare algorithmic approaches to solve the Preference Consistency Problem for preference statements based on hierarchical models. Instances of this problem contain a set of preference statements that are…
Submodular function maximization has been studied extensively in recent years under various constraints and models. The problem plays a major role in various disciplines. We study a natural online variant of this problem in which elements…
Algorithm selection is crucial in the field of optimization, as no single algorithm performs perfectly across all types of optimization problems. Finding the best algorithm among a given set of algorithms for a given problem requires a…
Classically, a mainstream approach for solving a convex-concave min-max problem is to instead solve the variational inequality problem arising from its first-order optimality conditions. Is it possible to solve min-max problems faster by…
Many applications, e.g., Web service composition, complex system design, team formation, etc., rely on methods for identifying collections of objects or entities satisfying some functional requirement. Among the collections that satisfy the…
This paper explores some sufficient conditions for the enhanced solvability of strong vector equilibrium problems, which can be established via a variational approach. Enhanced solvability here means existence of solutions, which are strong…
In this paper, we study a maximization problem on real sequences. More precisely, for a given sequence, we are interested in computing the supremum of the sequence and an index for which the associated term is maximal. We propose a general…
The main purpose of this paper is to propose a variance-based Bregman extragradient algorithm with line search for solving stochastic variational inequalities, which is robust with respect an unknown Lipschitz constant. We prove the almost…
We consider manipulation strategies for the rank-maximal matching problem. In the rank-maximal matching problem we are given a bipartite graph $G = (A \cup P, E)$ such that $A$ denotes a set of applicants and $P$ a set of posts. Each…