New Variant of the Semi-Monotonic Augmented Lagrangian Algorithm

SMALE is an efficient algorithm for solving quadratic programming problems with simple bounds and linear equality constraints.There are two variants of this method: one updates the parameter for precision control of an inner solver by a factor less than one (the preferable variant, as it does not change the Hessian via penalty update), and the other updates the penalty by a factor greater than one (resulting in a lower number of outer iterations and fewer Hessian multiplications in the inner solver).We use the MPRGP algorithm as an inner solver for solving bound-constrained quadratic programming problems.We introduce a new theoretically supported variant that updates both these parameters: multiplying the penalty by a factor greater than one and multiplying the parameter for precision control for the MPRGP stopping criterion by the square root of this factor.The larger penalty accelerates the outer loop, while the larger parame-1