Vector Optimization

A new era is emerging in which a group of quantitative methods featuring characteristics of multidimensional comparative analysis (MCA) and multi-criteria decision-making analysis (MCDA) can be used to automate objective decision-making processes.

This book presents the mathematical theory of vector variational inequalities and their relations with vector optimization problems. It is the first-ever book to introduce well-posedness and sensitivity analysis for vector equilibrium problems.

This book investigates several duality approaches for vector optimization problems, while also comparing them. Special attention is paid to duality for linear vector optimization problems, for which a vector dual that avoids the shortcomings of the c

Set-valued optimization is a vibrant and expanding branch of mathematics that deals with optimization problems where the objective map and/or the constraints maps are set-valued maps acting between certain spaces. Since set-valued maps subsumes singl

This book provides an introduction to vector optimization with variable ordering structures, i.e., to optimization problems with a vector-valued objective function where the elements in the objective space are compared based on a variable ordering st

We always come cross several decision-making problems in our daily life. Such problems are always conflicting in which many different view points should be satisfied. In politics, business, industrial systems, management science, networks, etc. one o

The theory of Vector Optimization is developed by a systematic usage of infimum and supremum. In order to get existence and appropriate properties of the infimum, the image space of the vector optimization problem is embedded into a larger space, whi

Many kinds of practical problems such as engineering design, industrial m- agement and ?nancial investment have multiple objectives con?icting with eachother. Thoseproblemscanbeformulatedasmultiobjectiveoptimization. In multiobjective optimization, t