A quadratically convergent line-search algorithm for pice wise smooth convex optimization^*

^*This work was supported in part by the Russian Foundation for Fundamental Research under the grant 94-01-01771

Abstract

A quadratically convergent line-search algorithm for piecewise smooth convex optimization based on a discontinuous piecewise linear approximation of the subgradient of the objective function is proposed. The algorithm safeguards the optimal point and has a global linear rate of convergence with locally quadratic convergence in the case of an isolated non-degenerate kink at the solution. For practical purposes it can be combined with the line-search routine based on cubic approximation of the objective function to produce an algorithm suitable for both smooth and nonsmooth optimization

Keywords:

• Line-Search
• Convex Nondifferentiable Optimization

^*This work was supported in part by the Russian Foundation for Fundamental Research under the grant 94-01-01771

^*This work was supported in part by the Russian Foundation for Fundamental Research under the grant 94-01-01771

Notes

^*This work was supported in part by the Russian Foundation for Fundamental Research under the grant 94-01-01771