vector optimization – Page 3 – Optimization Online

Inferring efficient weights from pairwise comparison matrices

Published: 2003/12/04

Multi-Criteria Optimization analytic hierarchy process, eigenvector method, multiobjective fractional programming, vector optimization

Several Multi-Criteria-Decision-Making methodologies assume the existence of weights associated with the different criteria, reflecting their relative importance. One of the most popular ways to infer such weights is the Analytic Hierarchy Process, which constructs first a matrix of pairwise comparisons, from which weights are derived following one out of many existing procedures, such as the … Read more

Optimality Conditions for Vector Optimization with Set-Valued Maps

Published: 2002/03/08, Updated: 2005/07/26

Yongwei Huang

Generalized Convexity/Monoticity, Multi-Criteria Optimization, Nonlinear Optimization near convexlikeness, near semiconvexlikeness, optimality conditions, set-valued maps, vector optimization, weak e-minimizers

Based on near convexity, we introduce the concepts of nearly convexlike set-valued maps and nearly semiconvexlike set-valued maps, give some charaterizations of them, and investigate the relationships between them. Then a Farkas-Minkowski type alternative theorem is shown under the assumption of near semiconvexlikeness. By using the alternative theorem and some other lemmas, we establish necessary … Read more