Semidifferential Calculus?

[Stephen Tashi]

I came across this announcement from SIAM (Society For Industrial And Applied Mathematics):

Announcing the 2012 publication by SIAM of:
Introduction to Optimization and Semidifferential Calculus, by M. C. Delfour

OK, I give. What is Semidifferential Calculus?

 

[pwsnafu]

I've seen fractional derivative of order 1/2 being called the semi-derivative before. Maybe that?

 

[Bacle2]

I think it may be a Calculus in which you allow for fractional derivatives, but I am not

sure.

 

[pwsnafu]

Apparently not:

Readers will find:
• an original and well integrated treatment of semidifferential calculus and optimization;
• emphasis on the Hadamard subdifferential, introduced at the beginning of the 20th century and somewhat overlooked for many years, with references to original papers by Hadamard (1923) and Fréchet (1925);
• fundamentals of convex analysis (convexification, Fenchel duality, linear and quadratic programming, two-person zero-sum games, Lagrange primal and dual problems, semiconvex and semiconcave functions);
• complete definitions, theorems, and detailed proofs, even though it is not necessary to work through all of them;
• commentaries that put the subject into historical perspective;
• numerous examples and exercises throughout each chapter, and answers to the exercises provided in an appendix.

Yeah I'm lost

Edit:

According to this PDF it sounds like its something they can actually measure in experiments:

Semidifferential electroanalytical method was first introduced in 1975 by Goto and
Ishii⁶ based on the semiintegral electroanalysis method. It measures the
semidifferential of current against the electrode potential. In the case of the reversible
electrode reaction the following relationship between the electrode potential, E, and the
semiintegral of current, m, applies for a planar electrode and a ramp signal⁷:

Edit 2: Seems to be related to the subderivative in convex analysis.

 

[blue_raver22]

Semidifferential calculus is a branch of mathematics that deals with the study of optimization problems, specifically those involving nonsmooth functions. It extends the traditional differential calculus to handle functions that are not differentiable at certain points, such as those with corners or jumps. This is important in many real-world applications, particularly in engineering and economics, where optimization problems often involve nonsmooth functions. The publication of Introduction to Optimization and Semidifferential Calculus by SIAM is a valuable resource for those working in these fields, as it provides a comprehensive introduction to this important area of mathematics.