A Family of Multi-Step Subgradient Minimization Methods

For solving non-smooth multidimensional optimization problems, we present a family of relaxation subgradient methods (RSMs) with built-in algorithm for finding the descent direction that forms an acute angle all subgradients in neighborhood current minimum. Minimizing function along opposite (with minus sign) enables to go beyond The algorithms is based on systems inequalities. finite convergence separable bounded sets proved. Algorithms inequalities are used organize RSM family. On quadratic functions, equivalent conjugate gradient method (CGM). intended high-dimensional problems and studied theoretically numerically. Examples convex non-convex smooth large dimensions given.