Unified approaches to nonlinear optimization

This paper investigates and unifies several relative nonlinear optimization problems in locally convex topological vector spaces or in convex spaces. The main generalization including some unified forms is the weaking of convex-valued multifunctions to acyclic multifunctions and the relaxation of the compactness condition on constraint regions. The aim of this paper is to develop as consequences of fixed point theory a variety of existence results relevant to coincidence theorems, generalized KKM type theorems and some unified variational inequalities including quasi-variational inequalities without monotonicity nor metrizability.