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Ekeland Variational Principle

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  • Bruce C. Dieffenbach

    (Independent author)

Abstract

The standard variational principle is the first-order condition for an optimum. If the optimum is not attained, however, then the first-order condition fails to hold. At an approximate minimum, an approximate first-order condition need not hold. Perhaps the function is not subdifferentiable, or perhaps there is no small subgradient. Given an approximate minimum, the Ekeland variational principle considers a slight variation of the original problem. This variational problem has a minimum that is an appproximate minimum for the original problem. It satisfies an approximate first-order condition for the original problem, and its location is near the approximate minimum. This chapter proves the Ekeland variational principle for a convex optimization, via perturbation duality.

Suggested Citation

  • Bruce C. Dieffenbach, 2026. "Ekeland Variational Principle," Contributions to Economics,, Springer.
    • Handle: RePEc:spr:conchp:978-3-032-21396-9_32
    DOI: 10.1007/978-3-032-21396-9_32
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