On variational approach to economic equilibrium — type problem
Naniewicz, Zdzisław, Magdalena Nockowska‐Rosiak · PUBLISHING HOUSE OF THE UNIVERSITY OF SILESIA (University of Silesia) · 2006
The paper deals with an optimization problem in which minima of a finite collection of objective functions satisfy some unilateral constraints and are linked together by a certain subdifferential law. The governing relations are variational inequalities defined on a nonconvex feasible set. By reducing the problem to a variational inequality involving nonmonotone multivalued mapping defined over a nonnegative orthant, the existence of solutions is established under the assumption that constrained functions are positive homogeneous of degree at most one.