By V. Jeyakumar, Dinh The Luc
A fresh major innovation in mathematical sciences has been the revolutionary use of nonsmooth calculus, an extension of the differential calculus, as a key device of recent research in lots of parts of arithmetic, operations examine, and engineering. targeting the examine of nonsmooth vector capabilities, this e-book provides a complete account of the calculus of generalized Jacobian matrices and their purposes to non-stop nonsmooth optimization difficulties and variational inequalities in finite dimensions.
The therapy is stimulated by way of a wish to disclose an straight forward method of nonsmooth calculus through the use of a suite of matrices to interchange the nonexistent Jacobian matrix of a continuing vector functionality. this type of set of matrices types a brand new generalized Jacobian, known as pseudo-Jacobian. a right away extension of the classical by-product that follows uncomplicated ideas of calculus, the pseudo-Jacobian offers an axiomatic method of nonsmooth calculus, a versatile instrument for dealing with nonsmooth non-stop optimization problems.
Illustrated via quite a few examples of recognized generalized derivatives, the paintings could function a worthwhile reference for graduate scholars, researchers, and utilized mathematicians who desire to use nonsmooth ideas and non-stop optimization to version and resolve difficulties in mathematical programming, operations learn, and engineering. Readers require just a modest historical past in undergraduate mathematical research to stick with the fabric with minimum effort.