New algorithm for polynomial spectral factorization with quadratic convergence. II
New algorithm for polynomial spectral factorization with quadratic convergence. I
Newton-Kantorovich method and its global convergence.
Newton-Krylov type algorithm for solving nonlinear least squares problems.
Newton's Method for Nonlinear Inequalities.
Nonlinear conjugate gradient methods
Modifications of nonlinear conjugate gradient method are described and tested.
Nonlinear conjugate gradient methods with sufficient descent condition for large-scale unconstrained optimization.
Nonlinear iterative methods and parallel computation
Nonlinear optimization using the generalized reduced gradient method
Nonlinear Rescaling Method and Self-concordant Functions
Nonlinear rescaling is a tool for solving large-scale nonlinear programming problems. The primal-dual nonlinear rescaling method was used to solve two quadratic programming problems with quadratic constraints. Based on the performance of primal-dual nonlinear rescaling method on testing problems, the conclusions about setting up the parameters are made. Next, the connection between nonlinear rescaling methods and self-concordant functions is discussed and modified logarithmic barrier function is...
Nonlinear Successive Over-Relaxation.
Nonmonotone strategy for minimization of quadratics with simple constraints
An algorithm for quadratic minimization with simple bounds is introduced, combining, as many well-known methods do, active set strategies and projection steps. The novelty is that here the criterion for acceptance of a projected trial point is weaker than the usual ones, which are based on monotone decrease of the objective function. It is proved that convergence follows as in the monotone case. Numerical experiments with bound-constrained quadratic problems from CUTE collection show that the modified...
Non-monotoneous parallel iteration for solving convex feasibility problems
The method of projections onto convex sets to find a point in the intersection of a finite number of closed convex sets in an Euclidean space, sometimes leads to slow convergence of the constructed sequence. Such slow convergence depends both on the choice of the starting point and on the monotoneous behaviour of the usual algorithms. As there is normally no indication of how to choose the starting point in order to avoid slow convergence, we present in this paper a non-monotoneous parallel algorithm...
Note sur la convergence de méthodes de directions conjuguées
Numerical behavior of the method of projection onto an acute cone with level control in convex minimization
We present the numerical behavior of a projection method for convex minimization problems which was studied by Cegielski [1]. The method is a modification of the Polyak subgradient projection method [6] and of variable target value subgradient method of Kim, Ahn and Cho [2]. In each iteration of the method an obtuse cone is constructed. The obtuse cone is generated by a linearly independent system of subgradients. The next approximation of a solution is the projection onto a translated acute cone...
Numerical solution of some classes of complementarity and variational problems via dualization