By means of a conjugation scheme based on generalized convex conjugation theory instead of Fenchel conjugation, we build an alternative dual problem, using the perturbational approach, for a general optimization one defined on a separated locally convex topological space. Conditions guaranteeing strong duality for disturbed primal problems by continuous linear functionals and their respective dual problems, which is named stable strong duality, are stablished. In these conditions, the evenly

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... vexity of the perturbation function will play a fundamental role. Stable strong duality will also be studied in particular for Fenchel and Lagrange primal-dual problems, obtaining a characterization for Fenchel case.