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, which is a subset of the power set, in fact, the space of self-infimal sets. Based on this idea we establish solution concepts, existence and duality results and algorithms for the linear case. The main advantage of this approach is the high degree of analogy to corresponding results of Scalar Optimization. The concepts and results are used to explain and to improve practically relevant algorithms for linear vector optimization problems.
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, which is a subset of the power set, in fact, the space of self-infimal sets. Based on this idea we establish solution concepts, existence and duality results and algorithms for the linear case. The main advantage of this approach is the high degree of analogy to corresponding results of Scalar Optimization. The concepts and results are used to explain and to improve practically relevant algorithms for linear vector optimization problems.
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...
These notes grew out of a series of lectures given by the author at the Univer sity of Budapest during 1985-1986. Additional results have been included which were obtained while the author was at...
Preliminaries on convex analysis and vector optimization.- Conjugate duality in scalar optimization.- Conjugate vector duality via scalarization.- Conjugate duality for vector optimization problems...
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,...
Generalized Convex Functions.- Generalized Type I and Related Functions.- Optimality Conditions.- Duality Theory.- Second and Higher Order Duality.- Symmetric Duality.- Vector Variational-like...
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