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Numerical methods for nondifferentiable convex optimization. (English) Zbl 0616.90052

We study the proximal method, within a nonexact form for nonsmooth programming. We give a new algorithm, related to the cutting plane method for minimizing on \({\mathbb{R}}^ N\) a convex function that is a sum of a Legendre convex differentiable function and a nondifferentiable convex function. This algorithm is then used to solve nonsmooth convex optimization problems in the unconstrained and the constrained cases.

MSC:

90C25 Convex programming
90C55 Methods of successive quadratic programming type
65K05 Numerical mathematical programming methods
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