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This chapter deals with the task of minimizing a class of locally Lipschitz functions over closed sets. The focus is given to local-solution methods for structured non-smooth and non-convex problems. Structures of interest include Difference-of-Convex (DC) and difference of Convex and weakly Convex (CwC) optimization problems. The chapter starts by revisiting the generalized Frank-Wolfe method, passing through the DC algorithm to more sophisticated bundle methods for problems whose objective and non-linear constraint can be expressed as CwC functions.

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Methods for Non-smooth Non-convex Optimization

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  • 发表日期：

    2025年

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  • Wim Stefanus van Ackooij,
  • Welington Luis de Oliveira

摘要

This chapter deals with the task of minimizing a class of locally Lipschitz functions over closed sets. The focus is given to local-solution methods for structured non-smooth and non-convex problems. Structures of interest include Difference-of-Convex (DC) and difference of Convex and weakly Convex (CwC) optimization problems. The chapter starts by revisiting the generalized Frank-Wolfe method, passing through the DC algorithm to more sophisticated bundle methods for problems whose objective and non-linear constraint can be expressed as CwC functions.