The present lecture note is dedicated to the study of the optimality
conditions and the duality results for nonlinear vector optimization
problems, in ?nite and in?nite dimensions. The problems include are
nonlinear vector optimization problems, s- metric dual problems,
continuous-time vector optimization problems, relationships between
vector optimization and variational inequality problems. Nonlinear
vector optimization problems arise in several contexts such as in the
building and interpretation of economic models; the study of various
technolo- cal processes; the development of optimal choices in ?nance;
management science; production processes; transportation problems and
statistical decisions, etc. In preparing this lecture note a special
effort has been made to obtain a se- contained treatment of the
subjects; so we hope that this may be a suitable source for a beginner
in this fast growing area of research, a semester graduate course in
nonlinear programing, and a good reference book. This book may be useful
to theoretical economists, engineers, and applied researchers involved
in this area of active research. The lecture note is divided into eight
chapters: Chapter 1 brie?y deals with the notion of nonlinear programing
problems with basic notations and preliminaries. Chapter 2 deals with
various concepts of convex sets, convex functions, invex set, invex
functions, quasiinvex functions, pseudoinvex functions, type I and
generalized type I functions, V-invex functions, and univex functions.