Ekeland Variational Principle

Bruce C. Dieffenbach ()
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Bruce C. Dieffenbach: Independent author

Chapter 32 in Conjugate Duality in Economic Analysis, 2026, pp 239-242 from Springer

Abstract: 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.

Date: 2026
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DOI: 10.1007/978-3-032-21396-9_32

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