Abstract
The nonlinear conjugate gradient algorithms are a very effective way in solving large-scale unconstrained optimization problems. Based on some famous previous conjugate gradient methods, a modified hybrid conjugate gradient method was proposed. The proposed method can generate decent directions at every iteration independent of any line search. Under the Wolfe line search, the proposed method possesses global convergence. Numerical results show that the modified method is efficient and robust.
Highlights
Consider the following unconstrained optimization problem: min f(x), x∈Rn (1)where x ∈ Rn is a real vector with n ≥ 1 component and f: Rn ⟶ R is a smooth function and its gradient g(x) ≜ ∇f(x) is available
Global Convergence of Algorithm is section is devoted to the global convergence of algorithm framework under the Wolfe line search condition, i.e., the step length αk is yielded by condition (4)
To visualize the whole behaviour of the algorithms, we use the performance profiles proposed by Dolan and More [22] to compare the performance based on the CPU time, the number of function evaluation, the number of gradient evaluation, and the number of iteration, respectively
Summary
Received 14 January 2021; Revised 3 February 2021; Accepted 5 February 2021; Published 23 February 2021. E nonlinear conjugate gradient algorithms are a very effective way in solving large-scale unconstrained optimization problems. Based on some famous previous conjugate gradient methods, a modified hybrid conjugate gradient method was proposed. E proposed method can generate decent directions at every iteration independent of any line search. Under the Wolfe line search, the proposed method possesses global convergence. Numerical results show that the modified method is efficient and robust
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