A general theory of surrogate dual and perturbational extended surrogate dual optimization problems.

*(English)*Zbl 0607.90089Many duality concepts exist in optimization theory, each having its own advantage. However, for a good general duality theory it is desirable to have either a system of dependences between the different dualities or even a (or some) unified hypertheory. The author studies two completely different general concepts of dual problems to a given primal problem in locally convex spaces and also discusses a series of realizations of his concepts. The first one works with a one-parameter family of surrogate constraint sets, the second one at first uses a perturbational functional (and then also some surrogate constraint sets). No conjugation is involved. At the end of his paper the author announces a paper in which he has constructed a unified theory of optimization problems, which encompasses many of the known duality concepts as particular cases.

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