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Survey of Bundle Methods for Nonsmooth Optimization

Bundle methods are at the moment the most efficient and promising methods for nonsmooth optimization. They have been successfully used in many practical applications, for example, in economics, mechanics, engineering and optimal control. The aim of this paper is to give an overview of the development and history of the bundle methods from the seventies to the present. For simplicity, we first concentrate on the convex unconstrained case with a single objective function. The methods are later extended to nonconvex, constrained and multicriteria cases.