Subdifferential Calculus

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

Chapter 23 in Conjugate Duality in Economic Analysis, 2026, pp 169-179 from Springer

Abstract: Abstract Subdifferential calculus expresses one subdifferential in terms of another. To derive results of subdifferential calculus directly from the directional derivative is a powerful technique. For example, under general conditions, the subdifferential of a sum is the sum of the subdifferentials. For this example, the primal calculates the conjugate of the directional derivative of the sum of two functions; the value function is the indicator of the subdifferential of the sum. In the dual, the value function is the indicator of the sum of the subdifferentials. Under general conditions there is no duality gap, and the result follows. Using this same technique, we derive various results of subdifferential calculus. The procedure exemplifies how duality leads naturally to the discovery of a result. Calculating the dual discovers an alternate formula for the subdifferential.

Date: 2026
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DOI: 10.1007/978-3-032-21396-9_23

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