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<p>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.</p>

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Optimality Conditions and Subdifferential Calculus for Infinite Sums of Functions

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年2月3日

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  • Abderrahim Hantoute,
  • Alexander Y. Kruger,
  • Marco A. López

摘要

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.