Quantum Variant of Dai Yuan Conjugate Gradient Method

This is well-known that Fletcher and Powell (1963) and Dai and Yuan (1999) conjugate gradient methods have good convergence properties. Al-Baali (1985) used the Wolf line search conditions with the parameter \(0<\mathbb {\sigma }<\frac{1}{2}\) to satisfy the sufficient condition and converge globally for FR method. Hager and Zhang (2005) developed a new line search technique to attain the efficiency of the algorithm by exploiting the properties of linear that interpolates in a neighborhood of a local minimum. The global convergence of the Liu-Storey method was proposed by Tang et al. (2007)). Further Dai (2011) proposed the modified Hestenes-Stiefel type conjugate gradient formulas and verified the global convergence schemes through several test problems. In the same lines, many researchers have extensively studied the global convergence of several modified conjugate gradient methods for improving the numerical computations (Dai and Yuan 1999; Dai 2011; Dai and Wen 2012; Jiang et al. 2012; Jiang and Jian 2013).