subgradient method

In this paper, a problem whose cost function and constraints are increasing convex along rays is considered. For solving such problems, an algorithm is presented that is inspired by the generalized Cutting Angle Method. A set that contains the optimal solution of the mentioned problem is defined. Some numerical examples are presented to confirm the validity and accuracy of the algorithm.

We propose an iterative method that solves an unconstrained nonconvex nonsmooth optimization problem. The proposed method is a descent method that uses subgradients at each iteration and contains very simple procedures for finding descent directions and for solving line search subproblems. The convergence of the algorithms is studied