Let V be a finite set of n elements and F = {X1, X2, . . . , Xm} a family of m subsets of V. Two sets Xi and Xj of F overlap if Xi∩Xj 6= ∅, Xj \ Xi 6= ∅, and Xi \ Xj 6= ∅. Two sets X, Y ∈ F are in the same overlap class if there is a series X = X1, X2, . . . , Xk = Y of sets of F in which each XiXi+1 overlaps. In this note, we focus on efficiently identifying all overlap classes in O(n + ∑m i=1...

Over the past 20 years, development of offshore wind farms has become increasingly important across world. One most crucial reasons for that is turbines have higher average speeds than those onshore, producing more electricity. In this study, a new hybrid approach integrating Interval Rough Numbers (IRNs) into Best-Worst Method (BWM) and Measurement Alternatives Ranking according to Compromise ...

This research examines whether a low-status member in a high-status category (e.g., a low-end Audi) or a high-status member in a low-status category (e.g., a high-end Volkswagen) is favored when they are evaluated separately, holding the objective value of these items constant. Based on the research on brand equity, one might expect that an option introduced under a higher quality brand would g...

In this paper, we present a new primal-dual interior-point algorithm for linear optimization based on a trigonometric kernel function. By simple analysis, we derive the worst case complexity for a large-update primal-dual interior-point method based on this kernel function. This complexity estimate improves a result from [1] and matches the one obtained in [2].

In this paper we prove that the broad class of direct-search methods of directional type, based on imposing sufficient decrease to accept new iterates, exhibits the same worst case complexity bound and global rate of the gradient method for the unconstrained minimization of a convex and smooth function. More precisely, it will be shown that the number of iterations needed to reduce the norm of ...

In this paper we will discuss two variants of an inexact feasible interior point algorithm for convex quadratic programming. We will consider two different neighbourhoods: a (small) one induced by the use of the Euclidean norm which yields a short-step algorithm and a symmetric one induced by the use of the infinity norm which yields a (practical) long-step algorithm. Both algorithms allow for ...

for x 2 D D Œ0; 1 , 1; 2 2 R and d 2 N. Also, 1, ! 2, g, ̨0 and ! ̨1 are given functions from a weighted Korobov space. This problem describes several interesting physical and financial phenomena (see [7–9, 13, 14, 22]). On the other hand, the existence and uniqueness of the above problem were proved by many authors (see [3, 11, 12, 17, 18, 24]). The paper proposes a convergence analysis of disc...