A Modified Nonlinear Conjugate Gradient Algorithm for Large-Scale Nonsmooth Convex Optimization

A Modified Gradient Method for Distributionally Robust Logistic Regression over the Wasserstein Ball

“…In [37], a modified HS CG method for nonsmooth convex optimization problems was proposed, whose numerical efficiency was verified via high-dimensional training samples. Furthermore, in [38], a modified CG method that inherits the advantages of both HS and DY CG methods was constructed for a nonsmooth optimization problem. It is noted that the works in [37,38] merely addressed the convergence of the CG methods, while they ignored their convergence rates.…”

“…Furthermore, in [38], a modified CG method that inherits the advantages of both HS and DY CG methods was constructed for a nonsmooth optimization problem. It is noted that the works in [37,38] merely addressed the convergence of the CG methods, while they ignored their convergence rates. Thus, this paper aims to develop a modified CG method for the Wasserstein distributionally robust LR model under the FOBOS framework, which can not only prove its convergence but also estimates its convergence rate.…”

Solving large scale unconstrained optimization problems with an efficient conjugate gradient class

“…In addition to their original authors, the issue of global convergence of methods (5) has also been investigated by some researchers like Al-Baali [40] and Gilbert and Nocedal [41]. Likewise, for all the CG directions that are presented in previous paragraph, the authors proved global convergence under necessary line searches techniques such as Armijo [14,16,20,29], week Wolfe-Powell [15-18, 21, 23, 24, 26, 27, 30, 35], strong Wolfe-Powell [12,16,19,22,25,28,31], modifications of these three techniques [13,[32][33][34] or some backtracking algorithms [36][37][38][39].…”

“…For example, interested readers can see some modifications of HS method in [12,13], several combinations of FR method in [14][15][16], various developments of PRP method in [17][18][19][20][21], an extended LS method in [22] and variant improvements of DY method in [23][24][25]. Furthermore, some researchers used techniques like quasi-Newton [26][27][28], regularization [29,30], a combination of above methods [31][32][33] or alternative techniques [34,35] and introduced appropriate CG methods to solve optimization problems. Similarly, there exist plenty of CG algorithms that are created to solve systems of nonlinear equations [36][37][38][39].…”

Solving Large-Scale Unconstrained Optimization Problems with an Efficient Conjugate Gradient Class

“…For example, interested readers can see some modifcations of the HS method in the study by Faramarzi and Amini [11] and Hu et al [12], several combinations of the FR method in the work by Abubakar et al [13] and Sakai and Iiduka [14], various developments of the PRP method in the study by Mishra et al [15], Wu [16], and Andrei [17], an extended LS method in [18], and variant improvements of the DY method in the study by Deepho et al [19], Zhu et al [20], and Jiang and Jian [21]. Furthermore, some researchers used techniques such as quasi-Newton [22,23], regularization [24][25][26], a combination of above methods [27,28], or alternative techniques [29,30] and introduced appropriate CG methods to solve optimization problems. To discuss the CG methods in more detail, the readers can see [31].…”