A derivative-free trust-region algorithm for composite nonsmooth optimization

Abstract

The derivative-free trust-region algorithm proposed by Conn et al. (SIAM J Optim 20:387–415, 2009) is adapted to the problem of minimizing a composite function $$\varPhi (x)=f(x)+h(c(x))$$ , where $$f$$ and $$c$$ are smooth, and $$h$$ is convex but may be nonsmooth. Under certain conditions, global convergence and a function-evaluation complexity bound are proved. The complexity result is specialized to the case when the derivative-free algorithm is applied to solve equality-constrained problems. Preliminary numerical results with minimax problems are also reported.