The \(\mathcal{UV}\)-decomposition on a class of d.c. functions and optimality conditions (Q871665)

From the point of view of optimization, the first and second order expansions are mainly used for studying some optimality conditions and constructing algorithms. In this paper, the authors use \(\mathcal{U}\mathcal{V}\)-theory and \(\text{P}\)-differential calculus to study second order expansion of a class of D.C. functions and minimization problems. A \(\mathcal{U}\)-Lagrangian of this function is presented and some properties are given. The authors also present some necessary optimality conditions for a class of constrained D.C. minimization with linear constraints.