We present a new iterative method based on the line search filter method with the nonmonotone strategy to solve the system of nonlinear equations. The equations are divided into two groups; some equations are treated as constraints and the others act as the objective function, and the two groups are just updated at the iterations where it is needed indeed. We employ the nonmonotone idea to the ...

In the minimization of real valued functions, Newton’s algorithm is often combined with a line search method. Grippo et al [SIAM J. Numer. Anal., Vol. 23, No. 4] first suggested a nonmonotone stepsize selection rule based on the maximum of a fixed set of previous function values. In this paper we introduce the notion of relaxing functions and suggest several other nonmonotone procedures using a...

is satisfied, where σ is the noise level. Alternatively, the algorithm terminates when the maximum number of 400 ·n function evaluations is exceeded. For each problem, a series of 50 independent runs are conducted. We considered a test run successful if the stopping criterium (1) is satisfied before exceeding the maximal number of function evaluations. To compare the performance of methods from...

In this paper, we propose two limited memory BFGS algorithms with a nonmonotone line search technique for unconstrained optimization problems. The global convergence of the given methods will be established under suitable conditions. Numerical results show that the presented algorithms are more competitive than the normal BFGS method.

In this paper, an unconstrained minimization algorithm is defined in which a nonmonotone line search technique is employed in association with a truncated Newton algorithm. Numerical results obtained for a set of standard test problems are reported which indicate that the proposed algorithm is highly effective in the solution of illconditioned as well as of large dimensional problems.