Uncovers necessary conditions for local minima in infinite function sums, suggesting broader applications in optimization theory.
The paper extends the widely used in optimisation theory decoupling techniques to infinite collections of functions. Extended concepts of uniform lower semicontinuity and firm uniform lower semicontinuity are discussed. The main theorems give fuzzy subdifferential necessary conditions (multiplier rules) for a local minimum of the sum of an infinite collection of functions and fuzzy subdifferential sum rules without the traditional Lipschitz continuity assumptions. More subtle “quasi” versions of the uniform infimum and uniform lower semicontinuity properties are also discussed.
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Hantoute et al. (2026) studied this question.
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