This paper presents a hybrid ODE-based method for unconstrained optimization problems, which combines the idea of IMPBOT with the subspace technique and a fixed step-length. The main characteristic of this method is that at each iteration, a lower dimensional system of linear equations is solved...

Recently, conjugate gradient methods, which usually generate descent search directions, are useful for large-scale optimization. Narushima et al. (SIAM J Optim 21:212–230, <CitationRef CitationID="CR22">2011</CitationRef>) have proposed a three-term conjugate gradient method which satisfies a sufficient descent condition. We extend this...</citationref>

Conjugate gradient methods are efficient to minimize differentiable objective functions in large dimension spaces. Recently, Dai and Yuan introduced a tree-parameter family of nonlinear conjugate gradient methods and show their convergence. However, line search strategies usually bring...

In this paper, we present a new trust region method for unconstrained nonlinear programming in which we blend adaptive trust region algorithm by non-monotone strategy to propose a new non-monotone trust region algorithm with automatically adjusted radius. Both non-monotone strategy and adaptive...

The conjugate gradient method is widely used in unconstrained optimization, especially for large-scale problems. Recently, Zhang et al. proposed a three-term PRP method (TTPRP) and a three-term HS method (TTHS), both of which can produce sufficient descent conditions. In this paper, the global...

In this paper, we present an adaptive trust region method for solving unconstrained optimization problems which combines nonmonotone technique with a new update rule for the trust region radius. At each iteration, our method can adjust the trust region radius of related subproblem. We construct...