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Fundamentals of equilibrium problems. (English) Zbl 1099.91072
The paper under review is devoted to the general concept of equilibria and related theory, reflecting the problem of stability of situations in numerous economic, social, behavioral and technical problems. Some new classes of equilibrium problems are considered in the framework of convexity, invexity, g-convexity and prox-regular convexity. Several iterative schemes for solving such classes, based on the auxiliary principle techniques, are developed. The convergence phenomenon in the equilibrium models is analyzed and the concept of well-posedness for the equilibrium problem is introduced. The main results regard this concept and the impact of applications of variational inequalities.
MSC:
91B50General equilibrium theory in economics
91B52Special types of equilibria in economics
49J40Variational methods including variational inequalities
90C26Nonconvex programming, global optimization
90C30Nonlinear programming