A q-Polak–Ribière–Polyak conjugate gradient algorithm for unconstrained optimization problems

Mishra, Shashi Kant; Chakraborty, Suvra Kanti; Samei, Mohammad Esmael; Ram, Bhagwat

doi:10.1186/s13660-021-02554-6

Cited by 16 publications

(9 citation statements)

References 51 publications

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“…The temperature of 298 K and 1 bar of pressure were maintained throughout the simulation. At a long-range cutoff of 12.5 Å, the pressure and temperature were measured using a Nose Hoover thermostat and barostat, respectively. , Initially, the system underwent energy minimization with conjugate gradient (CG) algorithm with required cycles and followed by NVT ensemble for equilibration for 5 ns. Then, from the relaxed geometry, further production runs for both NVT and NPT ensembles were carried out for 20 ns with a time step of 0.1 fs.…”

Section: Methodsmentioning

confidence: 99%

Investigation of Guest-Induced Flexibility in Pyrazine Derivative of ALFFIVE MOF via Molecular Simulation

2023

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One of the important understandings of porous solids like metal−organic frameworks (MOFs) is their flexibility. Therefore, there are certain computational studies on flexible MOFs in the literature, primarily concentrating on MIL-53, UiO-66, and DUT-49. Here, investigation of another class of MOF, that is, [Ni(1,4-pyrazine) 2 (AlF 5 )] n , was shown to have guestinduced flexible characteristics; nevertheless, the mechanism for the emergence of flexibility is uncertain. We simulated the structural flexibility of [Ni(1,4pyrazine) 2 (AlF 5 )] n , named ALFFIVE-Ni-pyr-TBP, upon adsorption of a guest molecule based on force fields using the molecular dynamics (MD) method and Monte Carlo (MC) simulations. As the first step towards understanding guestinduced flexibility, the MC simulations were performed by relaxing the framework and then further comparing it with the rigid framework. Subsequently, MD simulations were executed on the ALFFIVE-Ni-pyr-TBP framework with and without the guest molecules. In the case of moisture adsorption, the MOF system was identified to undergo a geometric transformation from trigonal bipyramidal to square bipyramidal geometry due to the strong interaction of oxygen of the water with the metal aluminum. However, some tilting in the pyrazine ligand was observed in the presence of all the guest molecules. Therefore, the detailed guest-induced flexibility described in this work could support the ALFFIVE series to be explored for future adsorption applications.

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Section: Methodsmentioning

confidence: 99%

Investigation of Guest-Induced Flexibility in Pyrazine Derivative of ALFFIVE MOF via Molecular Simulation

2023

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“…The global convergence properties of the above methods in their continued version (i.e., without restarts) have been investigated by many authors, such that Zoutendijk, 40 Al‐ Baali, 41 Liu et al, 42 Powell, 43,46 Gilbert and Nocedal, 44 Dai and Yuan 45 . Recently, in Liu et al, 47 a q‐Polak‐Ribière method is provided, and global convergence is also established.…”

Section: A New Rate Of Convergence For Fletcher‐reeves Methods With I...mentioning

confidence: 99%

On the convergence rate of Fletcher‐Reeves nonlinear conjugate gradient methods satisfying strong Wolfe conditions: Application to parameter identification in problems governed by general dynamics

Riahi

Qattan

2021

Math Methods in App Sciences

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Over the last decades, many efforts have been made toward the understanding of the convergence rate of the gradient-based method for both constrained and unconstrained optimization. The cases of the strongly convex and weakly convex payoff function have been extensively studied and are nowadays fully understood. Despite the impressive advances made in the convex optimization context, the nonlinear non-convex optimization problems are still not fully exploited. In this paper, we are concerned with the nonlinear, non-convex optimization problem under system dynamic constraints. We apply our analysis to parameter identification of systems governed by general nonlinear differential equations. The considered inverse problem is presented using optimal control tools. We tackle the optimization through the use of Fletcher-Reeves nonlinear conjugate gradient method satisfying strong Wolfe conditions with inexact line search. We rigorously establish a convergence analysis of the method and report a new linear convergence rate which forms the main contribution of this work. The theoretical result reported in our analysis requires that the second derivative of the payoff functional be continuous and bounded. Numerical evidence on a selection of popular nonlinear models is presented as a direct application of parameter identification to support the theoretical findings.

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“…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].…”

Section: Introductionmentioning

confidence: 96%

“…Over the years, many researchers developed methods (5) and increased their efficiency in theoretical and numerical views. 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.…”

Section: Introductionmentioning

confidence: 99%

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

Bojari

Paripour

2023

Preprint

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‎The main goal of this paper is to introduce an appropriate conjugate gradient class to solve unconstrained optimization problems‎. ‎The presented class enjoys the benefits of having three free parameters‎, ‎its directions are descent and it can fulfill the Dai-Liao conjugacy condition‎. ‎Global convergence property of the new class is proved under weak-Wolfe-Powell line search technique‎. ‎Numerical efficiency of the proposed class is confirmed in two sets of experiments including 210 test problems and ten disparate conjugate gradient methods‎. 2020 MSC: 90C06, 90C30, 90C26

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A q-Polak–Ribière–Polyak conjugate gradient algorithm for unconstrained optimization problems

Cited by 16 publications

References 51 publications

Investigation of Guest-Induced Flexibility in Pyrazine Derivative of ALFFIVE MOF via Molecular Simulation

Investigation of Guest-Induced Flexibility in Pyrazine Derivative of ALFFIVE MOF via Molecular Simulation

On the convergence rate of Fletcher‐Reeves nonlinear conjugate gradient methods satisfying strong Wolfe conditions: Application to parameter identification in problems governed by general dynamics

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

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