Optimality conditions for pareto nonsmooth nonconvex programming in banach spaces

In this paper, we consider a vector optimization problem where all functions involved are defined on Banach spaces. We obtain necessary and sufficient criteria for optimality in the form of Karush-Kuhn-Tucker conditions. We also introduce a nonsmooth dual problem and provide duality theorems.

Discrete generator coordinate: Symmetry restoration in finite-dimensional spaces

Group theoretical-based techniques and fundamental results from number theory are used in order to allow for the construction of exact projectors in finite-dimensional spaces. These operators are shown to make use only of discrete variables, which play the role of discrete generator coordinates, and their application in the number symmetry restoration is carried out in a nuclear BCS wave function which explicitly violates that symmetry. © 1999 Published by Elsevier Science B.V. All rights reserved.