Armijo method is a kind of line search method that usually be used when look for the step size in nonlinear optimization. This paper makes the summary of its modified forms, and then the nonmonotone Armijo-type line search methods are proposed. The numerical results will show that some line search methods with the novel nonmonotone line search are available and efficient in practical computation.
[Show abstract][Hide abstract] ABSTRACT: The aim of this paper is to define a new class of minimization algorithms for solving large scale unconstrained problems. In particular we describe a stabilization framework, based on a curvilinear linesearch, which uses a combination of a Newton-type direction and a negative curvature direction. The motivation for using negative curvature direction is that of taking into account local nonconvexity of the objective function. On the basis of this framework, we propose an algorithm which uses the Lanczos method for determining at each iteration both a Newton-type direction and an effective negative curvature direction. The results of an extensive numerical testing is reported together with a comparison with the LANCELOT package. These results show that the algorithm is very competitive and this seems to indicate that the proposed approach is promising. 1 Introduction In this work, we deal with the definition of new efficient unconstrained minimization algorithms for solving large scal...
[Show abstract][Hide abstract] ABSTRACT: 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.
Journal of Optimization Theory and Applications 02/1989; 60(3):401-419. DOI:10.1007/BF00940345 · 1.51 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: In this paper acceptability criteria for the linesearch stepsize are introduced which require only function values. Simple
algorithm models based on these criteria are presented. Some modifications of criteria based on the knowledge of the directional
derivative are also illustrated.
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