Stabilization method for solving equilibrium programming problems with inaccurately defined initial data (Q5955521)

The problem of equilibrium programming: find the point \(v_{*}\) from the conditions \[ v_{*} \in W = \{w \in W_0: g_i(w)\leq 0, \;i=\overline{1, m},\;g_i(w)=0, i= \overline{m+1, s}\},\tag{1} \] \[ \Phi(v_*, v_*)\leq \Phi(v_*, w)\;\forall w \in W, \] where \(W_0\) is the given set of the Euclidean space \(E^n\) and the functions \(\Phi(v, w)\), \(g_i(w)\), \(i=\overline{1, s}\) are definite on the set \(W_0\) is considered. Many problems of operations research, mathematical programming, mathematical economics etc. can be reduced to the problem (1). For such a problem, it is possible to use the ideas and the methods of regularization and stabilization of unstable problems of mathematical programming. The stabilization method is suggested for solving equilibrium programming problems when not only a purpose function but also the set in which the point of equilibrium is being searched is not exactly given. The convergence of the method is considered. The regularization operator is constructed.