A new family of conjugate gradient methods

Abstract

a b s t r a c tIn this paper we develop a new class of conjugate gradient methods for unconstrained optimization problems. A new nonmonotone line search technique is proposed to guarantee the global convergence of these conjugate gradient methods under some mild conditions. In particular, Polak-Ribiére-Polyak and Liu-Storey conjugate gradient methods are special cases of the new class of conjugate gradient methods. By estimating the local Lipschitz constant of the derivative of objective functions, we can find an adequate step size and substantially decrease the function evaluations at each iteration. Numerical results show that these new conjugate gradient methods are effective in minimizing large-scale non-convex non-quadratic functions.

Molecular modeling of the binding modes of the iron-sulfur protein to the Jac1 co-chaperone from S accharomyces cerevisiae by all-atom and coarse-grained approaches

“…In the first step, the energy was minimized by the steepest‐descent and conjugate‐gradient algorithms. Combining these two algorithms provides the best results because the steepest‐descent algorithm is more efficient and stable when far from the minimum (therefore, it brings the system to the neighborhood of the minimum quickly), whereas the conjugated‐gradient is much more efficient in close proximity to the minimum . Subsequently, an all‐atom MD simulation was performed with the AMBER FF99SB force field and the TIP3P water model .…”

A new class of nonlinear conjugate gradient coefficients with exact and inexact line searches

“…Many researchers believe that the FR, DY, CD, PR, HS, and LS will behave differently when the function is non-quadratic and the exact line search is used (Shi and Guo [37], Yuan and Wei [6], Shi et al [38], and Dai [36]). In fact, in this study we show that the behaviour of these methods could be divided into two groups as shown by the performance profile.…”

“…For good references of CG methods with significant findings, please refer to Hager and Zhang [28], Sun and Zhang [11], Birgin and Martinez [3], Dai and Yuan [33], Yuan and Wei [6], Andrei [23], Shi and Guo [37], and Wei et al [39]. For a good compilation and comparative study of newer CG methods, please refer to Andrei [22,24] and Rivaie et al [18].…”

A new family of conjugate gradient methods for unconstrained optimization

“…The main reason is that it cannot guarantee the descent objective function values at each iteration (Hager and Zhang [11]). For further reading and recent finding of CG methods, please refer to Sun and Zhang [21], Birgin and Matrtinez [4], Dai and Yuan [7], Yuan and Wei [23], Andrei [3], Shi and Gao [20] and Mustafa. et.…”