Convergence properties of local solutions of sequences of mathematical programming problems in general spaces

AbstractThis paper gives several sets of sufficient conditions that alocal solutionxk exists of the problem $$\min _{R^k } f^k (x)$$ ,k=1, 2,..., such that {xk} has cluster points that arelocal solutions of a problem of the form minRf(x). The results are based on a well-known concept of topological, orpoint-wise convergence of the sets {Rk} toR. Such results have been used to construct and validate large classes of mathematical programming methods based on successive approximations of the problem functions. They are also directly applicable to parametric and sensitivity analysis and provide additional characterizations of optimality for large classes of nonlinear programming problems.