A variable target value method for nondifferentiable optimization

This paper presents a new Variable target value method (VTVM) that can be used in conjunction with pure or deflected subgradient strategies. The proposed procedure assumes no a priori knowledge regarding bounds on the optimal value. The target values are updated iteratively whenever necessary, depending on the information obtained in the process of the algorithm. Moreover, convergence of the sequence of incumbent solution values to a near-optimum is proved using popular, practically desirable step-length rules. In addition, the method also allows a wide flexibility in designing subgradient deflection strategies by imposing only mild conditions on the deflection parameter. Some preliminary computational results are reported on a set of standard test problems in order to demonstrate the viability of this approach.