Simultaneous Nonstationary Optimization, Estimation and Approximation Procedures

The main aim of this paper is to investigate those algorithmic procedures which solve optimization problems whilst either estimating the unknown parameters of these problems or approximating them by more simple problems. The problem of nonstationary optimization with time-varying functions and a set of optimal solutions (set of equilibria) is considered. The proposed solution technique is based on the application of nonmonotonic optimization procedures. We derive the convergence of such procedures by studying the Hausdorf distance between a current approximate solution and the set of E-optimal solutions. The Lipschitz continuity of the Hausdorf distance between sets of E-optimal solutions upon the parameters of the problem is also discussed.

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