فهرست نشریات علمی دسترسی آزاد ایران

The conjugate gradient ({CG}) method is one of the simplest and most widely used approaches for unconstrained optimization, and our focus is on two-dimensional problems with numerous practical applications. We devise three hybrid {CG} methods in which the hybrid parameter is constructed from the Barzilai–Borwein process, and in these hybrids, the weaknesses of each constituent method are mitigated by the strengths of the others. The conjugate gradient parameter is formed as a linear combination of two well-known CG parameters, blended by a scalar, enabling our new methods to solve the targeted problems efficiently. Under mild assumptions, we establish the descent property of the generated directions and prove the global convergence of the hybrid schemes. Numerical experiments on ten practical examples indicate that the proposed hybrid {CG} methods outperform standard {CG} methods for two-dimensional unconstrained optimization.