Towards Supremum-Sum Subdifferential Calculus Free of Qualification Conditions

Towards Supremum-Sum Subdifferential Calculus Free of Qualification Conditions

Subdifferential Calculus Rules for Supremum Functions in Convex Analysis

Extending and improving some recent results of Hantoute, López, and Zălinescu and others, we provide characterization conditions for subdifferential formulas to hold for the supremum function of a family of convex functions on a real locally convex space.

Subdifferential Calculus Rules in Convex Analysis: A Unifying Approach Via Pointwise Supremum Functions

We provide a rule to calculate the subdifferential of the pointwise supremum of an arbitrary family of convex functions defined on a real locally convex topological vector space. Our formula is given exclusively in terms of the data functions, and does not require any assumption either on the index set on which the supremum is taken or on the involved functions. Some other calculus rules, namel...

Weaker conditions for subdifferential calculus of convex functions

Article history: Received 21 June 2014 Accepted 21 May 2016 Available online 1 June 2016 Communicated by H. Brezis MSC: 26B05 26J25 49H05

Lower semicontinuous type regularity conditions for subdifferential calculus

We give a lower semicontinuous type regularity condition and a closedness type one which turn out to be necessary and sufficient for the fulfillment of two different formulae involving the εsubdifferential of a perturbation function, respectively. These regularity conditions prove to be sufficient also for having formulae for the classical subdifferential of a perturbation function. Some recent...