The spirit of the bundle method (cf. for instance, Kiwiel (1985), Lemaréchal (1989) and Zowe (1985)) is to solve a convex minimization problem by successive solutions of “approximative” surrogate problems. To be more precise, if we consider a problem of minimization of a Φ-convex function f: X → ℝ, then the original problem is substituted by a minimization a finite maximum of functions øj; ∈ Ф, j =1,...,m, which belong to an “envelope” of f.
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