For the minimization of nonsmooth quasidifferentiable functions methods have been defined which make use of a particular structure of the function itself. This usually takes to the knowledge that the quasidifferential is a convex hull of a finite set of gradients and then stopping optimality conditions are sure to be working. In this paper a method for minimizing a general quasidifferentiable function is presented which do not assume that the objective function has any particular structure apart to be quasidifferentiable. A finite set of computed directional derivatives are used to get an approximation of the quasidifferential. The test of optimality condition and the search for a direction of descent are implemented as the solution of convenient subproblems.
A gradient-like method for quasidifferentiable optimization
PERETTI, Alberto
2004-01-01
Abstract
For the minimization of nonsmooth quasidifferentiable functions methods have been defined which make use of a particular structure of the function itself. This usually takes to the knowledge that the quasidifferential is a convex hull of a finite set of gradients and then stopping optimality conditions are sure to be working. In this paper a method for minimizing a general quasidifferentiable function is presented which do not assume that the objective function has any particular structure apart to be quasidifferentiable. A finite set of computed directional derivatives are used to get an approximation of the quasidifferential. The test of optimality condition and the search for a direction of descent are implemented as the solution of convenient subproblems.
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