Optimality Conditions and Subdifferential Calculus for Infinite Sums of Functions
Abstract
Abstract 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.
Fields of Study & Subjects
Optimization and Variational Analysis
Risk and Portfolio Optimization
Fixed Point Theorems Analysis
Publication details
- Journal / source
- Journal of Optimization Theory and Applications
- Publisher
- Springer Science and Business Media LLC
- Volume
- 208
- Issue
- 3
- Publication date
- 3 February 2026
- Language
- EN