A Rank Two Algorithm for Unconstrained Minimization

A variable order algorithm for unconstrained minimization

A variable order algorithm is proposed for the rini^ization of a function cff several variables. This algorithm has an order of convergence *.s high as four, good accuracy, and features a scalar subproblem at each iteration which may be along curved trajectories in the space of the independent variables. Numerical results en five standard test problems indicate superior performance when compare...

A new hybrid conjugate gradient algorithm for unconstrained optimization

In this paper, a new hybrid conjugate gradient algorithm is proposed for solving unconstrained optimization problems. This new method can generate sufficient descent directions unrelated to any line search. Moreover, the global convergence of the proposed method is proved under the Wolfe line search. Numerical experiments are also presented to show the efficiency of the proposed algorithm, espe...

TARM: A Turbo-type Algorithm for Affine Rank Minimization

The affine rank minimization (ARM) problem arises in many real-world applications. The goal is to recover a low-rank matrix from a small amount of noisy affine measurements. The original problem is NP-hard, and so directly solving the problem is computationally prohibitive. Approximate low-complexity solutions for ARM have recently attracted much research interest. In this paper, we design an i...

Descent heuristics for unconstrained minimization

Semidefinite relaxations often provide excellent starting points for nonconvex problems with multiple local minimizers. This work aims to find a local minimizer within a certain neighborhood of the starting point and with a small objective value. Several approaches are motivated and compared with each other.

A modified secant method for unconstrained minimization